Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
19501	Verify the Identity	(cot(B)^2-cos(B)^2)/(csc(B)^2-1)=cos(B)^2	$\frac{\cot^{2} (B) - \cos^{2} (B)}{\csc^{2} (B) - 1} = \cos^{2} (B)$
19502	Verify the Identity	(cot(x)^2)/(csc(x))=(1-sin(x)^2)/(sin(x))	$\frac{\cot^{2} (x)}{\csc (x)} = \frac{1 - \sin^{2} (x)}{\sin (x)}$
19503	Verify the Identity	(csc(x)^2+2csc(x)-3)/(csc(x)^2-1)=(csc(x)+3)/(csc(x)+1)	$\frac{\csc^{2} (x) + 2 \csc (x) - 3}{\csc^{2} (x) - 1} = \frac{\csc (x) + 3}{\csc (x) + 1}$
19504	Verify the Identity	(csc(x)^2-cot(x)^2)/(cos(x))=tan(x)csc(x)	$\frac{\csc^{2} (x) - \cot^{2} (x)}{\cos (x)} = \tan (x) \csc (x)$
19505	Verify the Identity	(cot(t)^2)/(csc(t))=csc(t)-sin(t)	$\frac{\cot^{2} (t)}{\csc (t)} = \csc (t) - \sin (t)$
19506	Verify the Identity	(cos(x)^2-1)/(csc(x)^2)=cos(x)^2	$\frac{\cos^{2} (x) - 1}{\csc^{2} (x)} = \cos^{2} (x)$
19507	Verify the Identity	(csc(x)+cot(x))(csc(x)-cot(x))+tan(x)^2=1/(cos(x)^2)	$(\csc (x) + \cot (x)) (\csc (x) - \cot (x)) + \tan^{2} (x) = \frac{1}{\cos^{2} (x)}$
19508	Verify the Identity	(sin(x)-cos(x))^2=1-2sin(x)cos(x)	${(\sin (x) - \cos (x))}^{2} = 1 - 2 \sin (x) \cos (x)$
19509	Verify the Identity	((sin(x)-1)^2)/(1-sin(x)^2)=(1-sin(x))/(1+sin(x))	$\frac{{(\sin (x) - 1)}^{2}}{1 - \sin^{2} (x)} = \frac{1 - \sin (x)}{1 + \sin (x)}$
19510	Verify the Identity	(sin(B)-tan(B))^2=(tan(B)^2)(cos(B)-1)^2	${(\sin (B) - \tan (B))}^{2} = (\tan^{2} (B)) {(\cos (B) - 1)}^{2}$
19511	Verify the Identity	(sin(t)+cos(t))^2=1+sin(2t)	${(\sin (t) + \cos (t))}^{2} = 1 + \sin (2 t)$
19512	Verify the Identity	(cos(x/2)-sin(x/2))^2=1-sin(x)	${(\cos (\frac{x}{2}) - \sin (\frac{x}{2}))}^{2} = 1 - \sin (x)$
19513	Verify the Identity	(6sin(x)+6cos(x))^2=36+36sin(2x)	${(6 \sin (x) + 6 \cos (x))}^{2} = 36 + 36 \sin (2 x)$
19514	Verify the Identity	(sin(x)-cos(x))(sin(x)+cos(x))=1-2cos(x)^2	$(\sin (x) - \cos (x)) (\sin (x) + \cos (x)) = 1 - 2 \cos^{2} (x)$
19515	Verify the Identity	sin(pi/2-theta)=cos(theta)	$\sin (\frac{π}{2} - θ) = \cos (θ)$
19516	Verify the Identity	(1-tan(x))/(1+tan(x))=(1-sin(2x))/(cos(2x))	$\frac{1 - \tan (x)}{1 + \tan (x)} = \frac{1 - \sin (2 x)}{\cos (2 x)}$
19517	Verify the Identity	((sec(x)+tan(x))(sec(x)-tan(x)))/(csc(x))=sin(x)	$\frac{(\sec (x) + \tan (x)) (\sec (x) - \tan (x))}{\csc (x)} = \sin (x)$
19518	Verify the Identity	(cos(x)+1)/(sin(x)^3)=(csc(x))/(1-cos(x))	$\frac{\cos (x) + 1}{\sin^{3} (x)} = \frac{\csc (x)}{1 - \cos (x)}$
19519	Verify the Identity	(csc(a)+cot(a))/(csc(a)-cot(a))=(1+2cos(a)+(cos(a)^2))/(sin(a)^2)	$\frac{\csc (a) + \cot (a)}{\csc (a) - \cot (a)} = \frac{1 + 2 \cos (a) + (\cos^{2} (a))}{\sin^{2} (a)}$
19520	Verify the Identity	(tan(y)+cot(y))sin(y)cos(y)=1	$(\tan (y) + \cot (y)) \sin (y) \cos (y) = 1$
19521	Verify the Identity	(csc(x)+1)(csc(x)-1)=cot(x)^2	$(\csc (x) + 1) (\csc (x) - 1) = \cot^{2} (x)$
19522	Verify the Identity	(csc(x)+cot(x))(1-cos(x))=sin(x)	$(\csc (x) + \cot (x)) (1 - \cos (x)) = \sin (x)$
19523	Verify the Identity	(sec(x)+tan(x))(sec(x)-tan(x))=1	$(\sec (x) + \tan (x)) (\sec (x) - \tan (x)) = 1$
19524	Verify the Identity	(sec(x)-tan(x))(csc(x)+1)=cot(x)	$(\sec (x) - \tan (x)) (\csc (x) + 1) = \cot (x)$
19525	Verify the Identity	(sec(x)-tan(x))(sec(x)+tan(x))=1	$(\sec (x) - \tan (x)) (\sec (x) + \tan (x)) = 1$
19526	Verify the Identity	(csc(x)-1)(csc(x)+1)=cot(x)^2	$(\csc (x) - 1) (\csc (x) + 1) = \cot^{2} (x)$
19527	Verify the Identity	(cot(x)sin(x))(sec(x)-cos(x))=sin(x)^2	$(\cot (x) \sin (x)) (\sec (x) - \cos (x)) = \sin^{2} (x)$
19528	Verify the Identity	(1-cos(x))(1+cos(x))=1/(csc(x)^2)	$(1 - \cos (x)) (1 + \cos (x)) = \frac{1}{\csc^{2} (x)}$
19529	Verify the Identity	(1-cos(x)^2)(1+cos(x)^2)=2sin(x)^2-sin(x)^4	$(1 - \cos^{2} (x)) (1 + \cos^{2} (x)) = 2 \sin^{2} (x) - \sin^{4} (x)$
19530	Verify the Identity	(1-cos(x))(1+cos(x))=sin(x)^2	$(1 - \cos (x)) (1 + \cos (x)) = \sin^{2} (x)$
19531	Verify the Identity	(1+tan(u)^2)(1-sin(u)^2)=1	$(1 + \tan^{2} (u)) (1 - \sin^{2} (u)) = 1$
19532	Verify the Identity	(1-sin(2)0)(1+tan(2)0)=1	$(1 - \sin (2) \cdot 0) (1 + \tan (2) \cdot 0) = 1$
19533	Verify the Identity	(1-sin(a))(1+sin(a))=1/(sec(a)^2)	$(1 - \sin (a)) (1 + \sin (a)) = \frac{1}{\sec^{2} (a)}$
19534	Find the Complement	sin(75)	$\sin (75)$
19535	Find the Complement	sin(a+90)	$\sin (a + 90)$
19536	Verify the Identity	(1-sin(x)^2)(1+tan(x)^2)=1	$(1 - \sin^{2} (x)) (1 + \tan^{2} (x)) = 1$
19537	Verify the Identity	(1-sin(x)^2)csc(x)=cos(x)cot(x)	$(1 - \sin^{2} (x)) \csc (x) = \cos (x) \cot (x)$
19538	Verify the Identity	(1-cos(2x))/(cos(x)sin(x))=2tan(x)	$\frac{1 - \cos (2 x)}{\cos (x) \sin (x)} = 2 \tan (x)$
19539	Verify the Identity	(1-cos(2x))/(sin(2x))=(sin(2x))/(1+cos(2x))	$\frac{1 - \cos (2 x)}{\sin (2 x)} = \frac{\sin (2 x)}{1 + \cos (2 x)}$
19540	Verify the Identity	(1-cos(2x))/(sin(2x))=tan(x)	$\frac{1 - \cos (2 x)}{\sin (2 x)} = \tan (x)$
19541	Verify the Identity	(1+sin(x))/(1-sin(x))=(csc(x)+1)/(csc(x)-1)	$\frac{1 + \sin (x)}{1 - \sin (x)} = \frac{\csc (x) + 1}{\csc (x) - 1}$
19542	Verify the Identity	(1-cos(x))/(1+cos(x))=(cot(x)-csc(x))^2	$\frac{1 - \cos (x)}{1 + \cos (x)} = {(\cot (x) - \csc (x))}^{2}$
19543	Verify the Identity	(1-sin(x))/(cos(x))=sec(x)-tan(x)	$\frac{1 - \sin (x)}{\cos (x)} = \sec (x) - \tan (x)$
19544	Verify the Identity	(1-sin(x))/(sin(x)cot(x))=(cos(x))/(1+sin(x))	$\frac{1 - \sin (x)}{\sin (x) \cot (x)} = \frac{\cos (x)}{1 + \sin (x)}$
19545	Verify the Identity	(1-sin(t))/(1+sin(t))=(sec(t)-tan(t))^2	$\frac{1 - \sin (t)}{1 + \sin (t)} = {(\sec (t) - \tan (t))}^{2}$
19546	Verify the Identity	(1-sin(t))/(cos(t))=(cos(t))/(1+sin(t))	$\frac{1 - \sin (t)}{\cos (t)} = \frac{\cos (t)}{1 + \sin (t)}$
19547	Verify the Identity	(1-sec(x))/(1-cos(x))=-sec(x)	$\frac{1 - \sec (x)}{1 - \cos (x)} = - \sec (x)$
19548	Verify the Identity	(1-sec(x))/(1+sec(x))=(cos(x)-1)/(cos(x)+1)	$\frac{1 - \sec (x)}{1 + \sec (x)} = \frac{\cos (x) - 1}{\cos (x) + 1}$
19549	Verify the Identity	(1-sec(x))/(tan(x))+(tan(x))/(1-sec(x))=-2csc(x)	$\frac{1 - \sec (x)}{\tan (x)} + \frac{\tan (x)}{1 - \sec (x)} = - 2 \csc (x)$
19550	Evaluate	cot(2pi)	$\cot (2 π)$
19551	Verify the Identity	(1+cos(x))/(1-cos(x))=(sec(x)+1)/(sec(x)-1)	$\frac{1 + \cos (x)}{1 - \cos (x)} = \frac{\sec (x) + 1}{\sec (x) - 1}$
19552	Verify the Identity	(1+cos(-x))/(sin(x)-cos(x)sin(-x))=csc(x)	$\frac{1 + \cos (- x)}{\sin (x) - \cos (x) \sin (- x)} = \csc (x)$
19553	Verify the Identity	(1+csc(x))/(1-csc(x))+(1+sin(x))/(1-sin(x))=0	$\frac{1 + \csc (x)}{1 - \csc (x)} + \frac{1 + \sin (x)}{1 - \sin (x)} = 0$
19554	Verify the Identity	(1+csc(x))/(sec(x))=cos(x)+cot(x)	$\frac{1 + \csc (x)}{\sec (x)} = \cos (x) + \cot (x)$
19555	Verify the Identity	(1+sec(x))/(csc(x))=sin(x)tan(x)	$\frac{1 + \sec (x)}{\csc (x)} = \sin (x) \tan (x)$
19556	Verify the Identity	(1+sin(2x))/(sin(2x))=1+1/2*(sec(x)csc(x))	$\frac{1 + \sin (2 x)}{\sin (2 x)} = 1 + \frac{1}{2} \cdot (\sec (x) \csc (x))$
19557	Verify the Identity	(1+sin(a))/(1-sin(a))-(1-sin(a))/(1+sin(a))=4tan(a)sec(a)	$\frac{1 + \sin (a)}{1 - \sin (a)} - \frac{1 - \sin (a)}{1 + \sin (a)} = 4 \tan (a) \sec (a)$
19558	Verify the Identity	1/(1-cos(x))=(1+cos(x))/(sin(x)^2)	$\frac{1}{1 - \cos (x)} = \frac{1 + \cos (x)}{\sin^{2} (x)}$
19559	Verify the Identity	1/(1+cos(x))=(1-cos(x))/(sin(x)^2)	$\frac{1}{1 + \cos (x)} = \frac{1 - \cos (x)}{\sin^{2} (x)}$
19560	Verify the Identity	1/(1-cos(y)^2)=cot(y)^2+1	$\frac{1}{1 - \cos^{2} (y)} = \cot^{2} (y) + 1$
19561	Verify the Identity	1/(1-sin(y)^2)=1+tan(y)^2	$\frac{1}{1 - \sin^{2} (y)} = 1 + \tan^{2} (y)$
19562	Verify the Identity	1/(cot(x))+cot(x)=1	$\frac{1}{\cot (x)} + \cot (x) = 1$
19563	Verify the Identity	1/(cos(x)+1)+1/(cos(x)-1)=-2csc(x)cot(x)	$\frac{1}{\cos (x) + 1} + \frac{1}{\cos (x) - 1} = - 2 \csc (x) \cot (x)$
19564	Verify the Identity	1/(1-sin(x))=sec(x)^2+tan(x)sec(x)	$\frac{1}{1 - \sin (x)} = \sec^{2} (x) + \tan (x) \sec (x)$
19565	Verify the Identity	1/(1-sin(w))+1/(1+sin(w))=2*sec(w)^2	$\frac{1}{1 - \sin (w)} + \frac{1}{1 + \sin (w)} = 2 \cdot \sec^{2} (w)$
19566	Verify the Identity	1/(tan(x)+cot(x))=sin(x)cos(x)	$\frac{1}{\tan (x) + \cot (x)} = \sin (x) \cos (x)$
19567	Verify the Identity	1/(tan(x)+sec(x))=(cos(x))/(sin(x)+1)	$\frac{1}{\tan (x) + \sec (x)} = \frac{\cos (x)}{\sin (x) + 1}$
19568	Verify the Identity	1/(tan(x)csc(x)sin(x))=cot(x)	$\frac{1}{\tan (x) \csc (x) \sin (x)} = \cot (x)$
19569	Verify the Identity	1/(tan(b))+tan(b)=(sec(b)^2)/(tan(b))	$\frac{1}{\tan (b)} + \tan (b) = \frac{\sec^{2} (b)}{\tan (b)}$
19570	Verify the Identity	1/(sec(x)-1)-1/(sec(x)+1)=2cot(x)^2	$\frac{1}{\sec (x) - 1} - \frac{1}{\sec (x) + 1} = 2 \cot^{2} (x)$
19571	Verify the Identity	1/(sin(x))-1/(cos(x))=(cos(x)-sin(x))/(sin(x)cos(x))	$\frac{1}{\sin (x)} - \frac{1}{\cos (x)} = \frac{\cos (x) - \sin (x)}{\sin (x) \cos (x)}$
19572	Verify the Identity	1/(sec(x)+tan(x))+1/(sec(x)-tan(x))=2sec(x)	$\frac{1}{\sec (x) + \tan (x)} + \frac{1}{\sec (x) - \tan (x)} = 2 \sec (x)$
19573	Verify the Identity	1/(sec(x)-cos(x))=cot(x)csc(x)	$\frac{1}{\sec (x) - \cos (x)} = \cot (x) \csc (x)$
19574	Verify the Identity	1/(sin(x)+1)+1/(csc(x)+1)=1	$\frac{1}{\sin (x) + 1} + \frac{1}{\csc (x) + 1} = 1$
19575	Verify the Identity	1/(csc(x)-cot(x))=(1+cos(x))/(sin(x))	$\frac{1}{\csc (x) - \cot (x)} = \frac{1 + \cos (x)}{\sin (x)}$
19576	Verify the Identity	1/(sin(x))-sin(x)=cot(x)cos(x)	$\frac{1}{\sin (x)} - \sin (x) = \cot (x) \cos (x)$
19577	Verify the Identity	(2-sin(x)^2)/(cos(x))=sec(x)+cos(x)	$\frac{2 - \sin^{2} (x)}{\cos (x)} = \sec (x) + \cos (x)$
19578	Verify the Identity	(2cos(x)cot(x))/(1-sin(x))-2=2csc(x)	$\frac{2 \cos (x) \cot (x)}{1 - \sin (x)} - 2 = 2 \csc (x)$
19579	Verify the Identity	(1-tan(x))/(1+tan(x))=(cot(x)-1)/(cot(x)+1)	$\frac{1 - \tan (x)}{1 + \tan (x)} = \frac{\cot (x) - 1}{\cot (x) + 1}$
19580	Verify the Identity	(1-tan(x))/(1+tan(x))=(cot(x-1))/(cot(x+1))	$\frac{1 - \tan (x)}{1 + \tan (x)} = \frac{\cot (x - 1)}{\cot (x + 1)}$
19581	Verify the Identity	(1-tan(x))/(sin(x))=csc(x)-sec(x)	$\frac{1 - \tan (x)}{\sin (x)} = \csc (x) - \sec (x)$
19582	Verify the Identity	(2sin(b)-2sin(b)^2)/(cos(b))+cos(b)^2=sin(2b)+cos(2b)	$\frac{2 \sin (b) - 2 \sin^{2} (b)}{\cos (b)} + \cos^{2} (b) = \sin (2 b) + \cos (2 b)$
19583	Verify the Identity	(2sin(x)*cos(x)-cos(x))/(1-sin(x)+sin(x)^2-cos(x)^2)=cot(x)	$\frac{2 \sin (x) \cdot \cos (x) - \cos (x)}{1 - \sin (x) + \sin^{2} (x) - \cos^{2} (x)} = \cot (x)$
19584	Verify the Identity	(2sin(x)cot(x)+sin(x)-4cot(x)-2)/(2cot(x)+1)=sin(x)-2	$\frac{2 \sin (x) \cot (x) + \sin (x) - 4 \cot (x) - 2}{2 \cot (x) + 1} = \sin (x) - 2$
19585	Verify the Identity	(2sin(y+1))/(sin(2y)+cos(y))=sec(y)	$\frac{2 \sin (y + 1)}{\sin (2 y) + \cos (y)} = \sec (y)$
19586	Verify the Identity	(2tan(x))/(1-tan(x)^2)=9/4*tan(x)	$\frac{2 \tan (x)}{1 - \tan^{2} (x)} = \frac{9}{4} \cdot \tan (x)$
19587	Verify the Identity	(cos(x)(tan(x)-sec(x)))/(1-csc(x))=sin(x)	$\frac{\cos (x) (\tan (x) - \sec (x))}{1 - \csc (x)} = \sin (x)$
19588	Verify the Identity	b/(sin(88.1))=648/(sin(0.8))	$\frac{b}{\sin (88.1)} = \frac{648}{\sin (0.8)}$
19589	Verify the Identity	(ccos(48))/(ccos(48))=12/(cos(48))	$\frac{c \cos (48)}{c \cos (48)} = \frac{12}{\cos (48)}$
19590	Verify the Identity	(cos(x))/(sec(x))+(sin(x))/(csc(x))=sec(x)^2-tan(x)^2	$\frac{\cos (x)}{\sec (x)} + \frac{\sin (x)}{\csc (x)} = \sec^{2} (x) - \tan^{2} (x)$
19591	Verify the Identity	(5-5tan(x)^4)/(sec(x)^2)=5(1-tan(x)^2)	$\frac{5 - 5 \tan^{4} (x)}{\sec^{2} (x)} = 5 (1 - \tan^{2} (x))$
19592	Verify the Identity	(cos(2x)+cos(2x))/(sin(x))-(sin(2x)+sin(2x))/(cos(x))=(cos(4x))/(sin(x)cos(x))	$\frac{\cos (2 x) + \cos (2 x)}{\sin (x)} - \frac{\sin (2 x) + \sin (2 x)}{\cos (x)} = \frac{\cos (4 x)}{\sin (x) \cos (x)}$
19593	Verify the Identity	(cos(0))/(sec(0))+(sin(0))/(csc(0))=1	$\frac{\cos (0)}{\sec (0)} + \frac{\sin (0)}{\csc (0)} = 1$
19594	Verify the Identity	(cos(x))/(1-sin(x))-(1+sin(x))/(cos(x))=0	$\frac{\cos (x)}{1 - \sin (x)} - \frac{1 + \sin (x)}{\cos (x)} = 0$
19595	Verify the Identity	(cos(u)sec(u))/(tan(u))=cot(u)	$\frac{\cos (u) \sec (u)}{\tan (u)} = \cot (u)$
19596	Verify the Identity	(cos(x)cot(x))/(cot(x)-cos(x))=(cot(x)+cos(x))/(cos(x)cot(x))	$\frac{\cos (x) \cdot \cot (x)}{\cot (x) - \cos (x)} = \frac{\cot (x) + \cos (x)}{\cos (x) \cdot \cot (x)}$
19597	Verify the Identity	(cos(3x)-cos(7x))/(sin(3x)+sin(7x))=tan(2x)	$\frac{\cos (3 x) - \cos (7 x)}{\sin (3 x) + \sin (7 x)} = \tan (2 x)$
19598	Verify the Identity	(cos(u))/(1+tan(u))-(sin(u))/(1+cot(u))=cos(u)-sin(u)	$\frac{\cos (u)}{1 + \tan (u)} - \frac{\sin (u)}{1 + \cot (u)} = \cos (u) - \sin (u)$
19599	Verify the Identity	(cos(t))/(1+sin(t))+(1+sin(t))/(cos(t))=2sec(t)	$\frac{\cos (t)}{1 + \sin (t)} + \frac{1 + \sin (t)}{\cos (t)} = 2 \sec (t)$
19600	Verify the Identity	(cos(x)+sin(x))/(cos(x)-sin(x))-(cos(x)-sin(x))/(cos(x)+sin(x))=2tan(2x)	$\frac{\cos (x) + \sin (x)}{\cos (x) - \sin (x)} - \frac{\cos (x) - \sin (x)}{\cos (x) + \sin (x)} = 2 \tan (2 x)$