Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
19301	Verify the Identity	csc(x)^4-csc(x)^2=cot(x)^4+cot(x)^2	$\csc^{4} (x) - \csc^{2} (x) = \cot^{4} (x) + \cot^{2} (x)$
19302	Verify the Identity	csc(x)^4-cot(x)^4=(1+cos(x)^2)/(1-cos(x)^2)	$\csc^{4} (x) - \cot^{4} (x) = \frac{1 + \cos^{2} (x)}{1 - \cos^{2} (x)}$
19303	Verify the Identity	(csc(x))/(sec(x))+(cos(x))/(sin(x))=2cot(x)	$\frac{\csc (x)}{\sec (x)} + \frac{\cos (x)}{\sin (x)} = 2 \cot (x)$
19304	Verify the Identity	(csc(x))/(tan(x)+cot(x))=cos(x)	$\frac{\csc (x)}{\tan (x) + \cot (x)} = \cos (x)$
19305	Verify the Identity	(cot(x)-tan(x))/(sin(x)*cos(x))=csc(x)^2-sec(x)^2	$\frac{\cot (x) - \tan (x)}{\sin (x) \cdot \cos (x)} = \csc^{2} (x) - \sec^{2} (x)$
19306	Verify the Identity	(cot(x)-tan(x))/(sin(x)cos(x))=csc(x)^2-sec(x)^2	$\frac{\cot (x) - \tan (x)}{\sin (x) \cos (x)} = \csc^{2} (x) - \sec^{2} (x)$
19307	Verify the Identity	csc(x)^2=(cot(x))/(tan(x))+1	$\csc^{2} (x) = \frac{\cot (x)}{\tan (x)} + 1$
19308	Verify the Identity	(csc(x)-sin(x))/(csc(x))=cos(x)^2	$\frac{\csc (x) - \sin (x)}{\csc (x)} = \cos^{2} (x)$
19309	Verify the Identity	csc(x)^4-cot(x)^4=2csc(x)^2-1	$\csc^{4} (x) - \cot^{4} (x) = 2 \csc^{2} (x) - 1$
19310	Verify the Identity	csc(x)^4-2csc(x)^2+1=cot(x)^4	$\csc^{4} (x) - 2 \csc^{2} (x) + 1 = \cot^{4} (x)$
19311	Verify the Identity	(sec(x))/(csc(x))=tan(x)	$\frac{\sec (x)}{\csc (x)} = \tan (x)$
19312	Verify the Identity	(sec(x))/(csc(x)-cot(x))-(sec(x))/(csc(x)+cot(x))=2csc(x)	$\frac{\sec (x)}{\csc (x) - \cot (x)} - \frac{\sec (x)}{\csc (x) + \cot (x)} = 2 \csc (x)$
19313	Verify the Identity	csc(x)^2tan(x)-tan(x)=cot(x)	$\csc^{2} (x) \tan (x) - \tan (x) = \cot (x)$
19314	Verify the Identity	csc(x)^2-cos(x)sec(x)=cot(x)^2	$\csc^{2} (x) - \cos (x) \sec (x) = \cot^{2} (x)$
19315	Verify the Identity	csc(y)^2-csc(y)cot(y)=1/(1+cos(y))	$\csc^{2} (y) - \csc (y) \cot (y) = \frac{1}{1 + \cos (y)}$
19316	Verify the Identity	(sin(3x)-sin(x))/(cos(x)-cos(3x))=cot(2x)	$\frac{\sin (3 x) - \sin (x)}{\cos (x) - \cos (3 x)} = \cot (2 x)$
19317	Verify the Identity	(sin(A))/(1-cos(A))-cot(A)=csc(A)	$\frac{\sin (A)}{1 - \cos (A)} - \cot (A) = \csc (A)$
19318	Verify the Identity	(sin(a)+sin(3a))/(cos(a)+cos(3a))=tan(2a)	$\frac{\sin (a) + \sin (3 a)}{\cos (a) + \cos (3 a)} = \tan (2 a)$
19319	Verify the Identity	(sin(a-B))/(sin(a)cos(B))=1-cot(a)tan(B)	$\frac{\sin (a - B)}{\sin (a) \cos (B)} = 1 - \cot (a) \tan (B)$
19320	Verify the Identity	(sin(x))/(1+sin(x))-(sin(x))/(1-sin(x))=2tan(x)^2	$\frac{\sin (x)}{1 + \sin (x)} - \frac{\sin (x)}{1 - \sin (x)} = 2 \tan^{2} (x)$
19321	Verify the Identity	(sin(t))/(1-cos(t))=(1+cos(t))/(sin(t))	$\frac{\sin (t)}{1 - \cos (t)} = \frac{1 + \cos (t)}{\sin (t)}$
19322	Verify the Identity	(sin(A+B))/(sin(A-B))=(tan(A)+tan(B))/(tan(A)-tan(B))	$\frac{\sin (A + B)}{\sin (A - B)} = \frac{\tan (A) + \tan (B)}{\tan (A) - \tan (B)}$
19323	Verify the Identity	(sin(s)+sin(t))/(cos(s)+cos(t))=tan((s+t)/2)	$\frac{\sin (s) + \sin (t)}{\cos (s) + \cos (t)} = \tan (\frac{s + t}{2})$
19324	Verify the Identity	(sin(145))/500=(sin(20))/a	$\frac{\sin (145)}{500} = \frac{\sin (20)}{a}$
19325	Verify the Identity	(sin(15))/10=(sin(115))/b	$\frac{\sin (15)}{10} = \frac{\sin (115)}{b}$
19326	Verify the Identity	(sin(2x))/(1-cos(2x))=cot(x)	$\frac{\sin (2 x)}{1 - \cos (2 x)} = \cot (x)$
19327	Verify the Identity	(sin(3x)+cos(3x))/(cos(x)-sin(x))=1+2sin(2x)	$\frac{\sin (3 x) + \cos (3 x)}{\cos (x) - \sin (x)} = 1 + 2 \sin (2 x)$
19328	Verify the Identity	(sin(4x)+sin(2x))/(cos(4x)+cos(2x))=tan(3x)	$\frac{\sin (4 x) + \sin (2 x)}{\cos (4 x) + \cos (2 x)} = \tan (3 x)$
19329	Verify the Identity	(sin(2x)+1)/(cos(2x))=(cos(x)+sin(x))/(cos(x)-sin(x))	$\frac{\sin (2 x) + 1}{\cos (2 x)} = \frac{\cos (x) + \sin (x)}{\cos (x) - \sin (x)}$
19330	Verify the Identity	(sec(x)+tan(x))/(csc(x)+1)=tan(x)	$\frac{\sec (x) + \tan (x)}{\csc (x) + 1} = \tan (x)$
19331	Verify the Identity	(sec(x))/(tan(x)+cot(x))=sin(x)	$\frac{\sec (x)}{\tan (x) + \cot (x)} = \sin (x)$
19332	Verify the Identity	(sec(x))/(1-tan(x))=1/(cos(x)-sin(x))	$\frac{\sec (x)}{1 - \tan (x)} = \frac{1}{\cos (x) - \sin (x)}$
19333	Verify the Identity	(sec(A)-1)/(sec(A)+1)=(1-cos(A))/(1+cos(A))	$\frac{\sec (A) - 1}{\sec (A) + 1} = \frac{1 - \cos (A)}{1 + \cos (A)}$
19334	Verify the Identity	(sec(A)-csc(A))/(sec(A)+csc(A))=(tan(A)-1)/(tan(A)+1)	$\frac{\sec (A) - \csc (A)}{\sec (A) + \csc (A)} = \frac{\tan (A) - 1}{\tan (A) + 1}$
19335	Verify the Identity	(sec(a))/(csc(a))=tan(a)	$\frac{\sec (a)}{\csc (a)} = \tan (a)$
19336	Verify the Identity	(sec(B))/(cos(B))-(tan(B))/(cot(B))=1	$\frac{\sec (B)}{\cos (B)} - \frac{\tan (B)}{\cot (B)} = 1$
19337	Verify the Identity	sec(1)^2x-1=(sin(x)^2)/(cos(x)^2)	$\sec^{2} (1) x - 1 = \frac{\sin^{2} (x)}{\cos^{2} (x)}$
19338	Verify the Identity	sec(x)^2=1/(cos(x)^2)	$\sec^{2} (x) = \frac{1}{\cos^{2} (x)}$
19339	Verify the Identity	sec(x/2)^2=2/(1+cos(x))	$\sec^{2} (\frac{x}{2}) = \frac{2}{1 + \cos (x)}$
19340	Verify the Identity	sec(x)^4-tan(x)^4=sec(x)^2+tan(x)^2	$\sec^{4} (x) - \tan^{4} (x) = \sec^{2} (x) + \tan^{2} (x)$
19341	Verify the Identity	sec(x)^4-tan(x)^4=1+(sin(x)^2)/(cos(x)^2)	$\sec^{4} (x) - \tan^{4} (x) = 1 + \frac{\sin^{2} (x)}{\cos^{2} (x)}$
19342	Verify the Identity	sec(2x)^4=4	$\sec^{4} (2 x) = 4$
19343	Verify the Identity	sec(x)^4tan(x)^2=(tan(x)^2+tan(x)^4)sec(x)^2	$\sec^{4} (x) \tan^{2} (x) = (\tan^{2} (x) + \tan^{4} (x)) \sec^{2} (x)$
19344	Verify the Identity	sec(t)^4-tan(t)^4=2sec(t-1)^2	$\sec^{4} (t) - \tan^{4} (t) = 2 \sec^{2} (t - 1)$
19345	Verify the Identity	(csc(x))/(cot(x))=sec(x)	$\frac{\csc (x)}{\cot (x)} = \sec (x)$
19346	Verify the Identity	sec(x)^2+csc(x)^2=sec(x)^2*csc(x)^2	$\sec^{2} (x) + \csc^{2} (x) = \sec^{2} (x) \cdot \csc^{2} (x)$
19347	Verify the Identity	sec(x)^2-2=tan(x)^2	$\sec^{2} (x) - 2 = \tan^{2} (x)$
19348	Verify the Identity	sec(x)^2-2tan(x)=0	$\sec^{2} (x) - 2 \tan (x) = 0$
19349	Verify the Identity	cos(x)csc(x)^2-cos(x)=sin(x)tan(x)	$\cos (x) \csc^{2} (x) - \cos (x) = \sin (x) \tan (x)$
19350	Verify the Identity	cos(x)+2cos(x)sin(x)=0	$\cos (x) + 2 \cos (x) \sin (x) = 0$
19351	Verify the Identity	cos(x)+ square root of 2=-cos(x)	$\cos (x) + \sqrt{2} = - \cos (x)$
19352	Verify the Identity	cos(x)(2sin(x)+1)=0	$\cos (x) (2 \sin (x) + 1) = 0$
19353	Verify the Identity	cos(x)(cot(x)+tan(x))=csc(x)	$\cos (x) (\cot (x) + \tan (x)) = \csc (x)$
19354	Verify the Identity	cos(x)(csc(x)+tan(x))=cot(x)+sin(x)	$\cos (x) (\csc (x) + \tan (x)) = \cot (x) + \sin (x)$
19355	Verify the Identity	cos(x)(sec(x)+cos(x)*csc(x)^2)=csc(x)^2	$\cos (x) (\sec (x) + \cos (x) \cdot \csc^{2} (x)) = \csc^{2} (x)$
19356	Verify the Identity	cos(x)(tan(x)+2)(2tan(x)+1)=2sec(x)+5sin(x)	$\cos (x) (\tan (x) + 2) (2 \tan (x) + 1) = 2 \sec (x) + 5 \sin (x)$
19357	Verify the Identity	cos(pi+x)=-cos(x)	$\cos (π + x) = - \cos (x)$
19358	Verify the Identity	cos(t)cot(t)=(1-sin(t)^2)/(sin(t))	$\cos (t) \cot (t) = \frac{1 - \sin^{2} (t)}{\sin (t)}$
19359	Verify the Identity	cos(3t)=4cos(t)^3-3cos(t)	$\cos (3 t) = 4 \cos^{3} (t) - 3 \cos (t)$
19360	Verify the Identity	cos(4x)+cos(2x)=2-2sin(2x)^2-2sin(x)^2	$\cos (4 x) + \cos (2 x) = 2 - 2 \sin^{2} (2 x) - 2 \sin^{2} (x)$
19361	Verify the Identity	cos(40)=5/r	$\cos (40) = \frac{5}{r}$
19362	Verify the Identity	cos(3x)=1	$\cos (3 x) = 1$
19363	Verify the Identity	cos(2x)cos(x)-2sin(2x)sin(x)=0	$\cos (2 x) \cos (x) - 2 \sin (2 x) \sin (x) = 0$
19364	Verify the Identity	cos(3x)=cos(x)(cos(2x)-2sin(x)^2)	$\cos (3 x) = \cos (x) (\cos (2 x) - 2 \sin^{2} (x))$
19365	Verify the Identity	cos(90+x)=-sin(x)	$\cos (90 + x) = - \sin (x)$
19366	Verify the Identity	cos(B)cot(B)=csc(B)-sin(B)	$\cos (B) \cot (B) = \csc (B) - \sin (B)$
19367	Verify the Identity	cos(A+B)cos(A-B)=cos(A)^2-sin(B)^2	$\cos (A + B) \cos (A - B) = \cos^{2} (A) - \sin^{2} (B)$
19368	Verify the Identity	cos(a-b)=cos(a)cos(b)+sin(a)sin(b)	$\cos (a - b) = \cos (a) \cos (b) + \sin (a) \sin (b)$
19369	Verify the Identity	cos(A-B)-cos(A+B)=2sin(a)sin(b)	$\cos (A - B) - \cos (A + B) = 2 \sin (a) \sin (b)$
19370	Verify the Identity	cos(a+b)*cos(a-b)=cos(b)^2-sin(a)^2	$\cos (a + b) \cdot \cos (a - b) = \cos^{2} (b) - \sin^{2} (a)$
19371	Verify the Identity	cos(a+b)+cos(a+b)=2cos(a)cos(b)	$\cos (a + b) + \cos (a + b) = 2 \cos (a) \cos (b)$
19372	Verify the Identity	cos(520)=cos(20)	$\cos (520) = \cos (20)$
19373	Verify the Identity	cos(2x)=2sin(x)cos(x)	$\cos (2 x) = 2 \sin (x) \cos (x)$
19374	Verify the Identity	cos(2x)sin(5x)=1/2*(sin(7x)+sin(3x))	$\cos (2 x) \sin (5 x) = \frac{1}{2} \cdot (\sin (7 x) + \sin (3 x))$
19375	Verify the Identity	cos(2x)=1/2	$\cos (2 x) = \frac{1}{2}$
19376	Verify the Identity	cos(2x) = square root of 2-cos(2x)	$\cos (2 x) = \sqrt{2} - \cos (2 x)$
19377	Verify the Identity	cos(2x)=0	$\cos (2 x) = 0$
19378	Verify the Identity	cos(2x)=1-2sin(x)^2	$\cos (2 x) = 1 - 2 \sin^{2} (x)$
19379	Verify the Identity	cos(2x)=2cos(x-1)^2	$\cos (2 x) = 2 \cos^{2} (x - 1)$
19380	Verify the Identity	cos(2x)=9sin(x)-4	$\cos (2 x) = 9 \sin (x) - 4$
19381	Verify the Identity	cos(2a)=2cos(a)^2-1	$\cos (2 a) = 2 \cos^{2} (a) - 1$
19382	Verify the Identity	cos(x)-sin(x)=1	$\cos (x) - \sin (x) = 1$
19383	Verify the Identity	cos((7pi)/4+x)+sin((5pi)/4+x)=0	$\cos (\frac{7 π}{4} + x) + \sin (\frac{5 π}{4} + x) = 0$
19384	Verify the Identity	cos((3pi)/2+x)=-cos(x)	$\cos (\frac{3 π}{2} + x) = - \cos (x)$
19385	Verify the Identity	cos(-x)=-cos(x)	$\cos (- x) = - \cos (x)$
19386	Verify the Identity	cos(pi/2-x)cos(-x)=(sin(2x))/2	$\cos (\frac{π}{2} - x) \cos (- x) = \frac{\sin (2 x)}{2}$
19387	Verify the Identity	cos(0)=sin(0)cot(0)	$\cos (0) = \sin (0) \cot (0)$
19388	Verify the Identity	cos(180+x)=-cos(x)	$\cos (180 + x) = - \cos (x)$
19389	Verify the Identity	cos(180-x)=-cos(x)	$\cos (180 - x) = - \cos (x)$
19390	Verify the Identity	cos(x)=-0.744	$\cos (x) = - 0.744$
19391	Verify the Identity	cos(x)=0	$\cos (x) = 0$
19392	Verify the Identity	cos(-x)-sin(-x)=cos(x)+sin(x)	$\cos (- x) - \sin (- x) = \cos (x) + \sin (x)$
19393	Verify the Identity	cos(x-(5pi)/4)=-( square root of 2)/2*(cos(x)+sin(x))	$\cos (x - \frac{5 π}{4}) = - \frac{\sqrt{2}}{2} \cdot (\cos (x) + \sin (x))$
19394	Verify the Identity	cos(x)tan(x)=cos(x)	$\cos (x) \tan (x) = \cos (x)$
19395	Verify the Identity	cos(x+pi)=cos(x)	$\cos (x + π) = \cos (x)$
19396	Verify the Identity	cos(x+y)*cos(x-y)=cos(x)^2-sin(y)^2	$\cos (x + y) \cdot \cos (x - y) = \cos^{2} (x) - \sin^{2} (y)$
19397	Verify the Identity	cos(x+y)=cos(x)+cos(y)	$\cos (x + y) = \cos (x) + \cos (y)$
19398	Verify the Identity	cos(x+pi/4)+cos(x-pi/4) = square root of 2cos(x)	$\cos (x + \frac{π}{4}) + \cos (x - \frac{π}{4}) = \sqrt{2} \cos (x)$
19399	Verify the Identity	cot(x)=(sin(2x))/(1-cos(2x))	$\cot (x) = \frac{\sin (2 x)}{1 - \cos (2 x)}$
19400	Verify the Identity	cos(y)cos(x-y)-sin(y)sin(x-y)=cos(x)	$\cos (y) \cos (x - y) - \sin (y) \sin (x - y) = \cos (x)$