Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
19401	Verify the Identity	cot(x)(cot(x)+tan(x))=csc(x)^2	$\cot (x) (\cot (x) + \tan (x)) = \csc^{2} (x)$
19402	Verify the Identity	cos(x-2pi)=cos(x)	$\cos (x - 2 π) = \cos (x)$
19403	Verify the Identity	cos(x-y)+cos(x+y)=2cos(x)cos(y)	$\cos (x - y) + \cos (x + y) = 2 \cos (x) \cos (y)$
19404	Verify the Identity	cos(x-y)-cos(x+y)=2sin(x)sin(y)	$\cos (x - y) - \cos (x + y) = 2 \sin (x) \sin (y)$
19405	Verify the Identity	cot(x)sec(x)=csc(x)	$\cot (x) \sec (x) = \csc (x)$
19406	Verify the Identity	cot(x)=2cos(x)	$\cot (x) = 2 \cos (x)$
19407	Verify the Identity	cos(x+y)-cos(x-y)=2cos(x)cos(y)	$\cos (x + y) - \cos (x - y) = 2 \cos (x) \cos (y)$
19408	Verify the Identity	cot(x)-1=0	$\cot (x) - 1 = 0$
19409	Verify the Identity	cot(360)=1	$\cot (360) = 1$
19410	Verify the Identity	cot(3x)=1	$\cot (3 x) = 1$
19411	Verify the Identity	csc(theta)-sin(theta)=cot(theta)cos(theta)	$\csc (θ) - \sin (θ) = \cot (θ) \cos (θ)$
19412	Verify the Identity	csc(u)-cot(u)=(sin(u))/(1+cos(u))	$\csc (u) - \cot (u) = \frac{\sin (u)}{1 + \cos (u)}$
19413	Verify the Identity	csc(u)-sin(u)=cos(u)cot(u)	$\csc (u) - \sin (u) = \cos (u) \cot (u)$
19414	Verify the Identity	csc(x)*sec(x)=cot(x)+tan(x)	$\csc (x) \cdot \sec (x) = \cot (x) + \tan (x)$
19415	Verify the Identity	cot(x)-1=cos(x)(csc(x)-sec(x))	$\cot (x) - 1 = \cos (x) (\csc (x) - \sec (x))$
19416	Verify the Identity	cot(-x)cos(-x)+sin(-x)=-csc(x)	$\cot (- x) \cos (- x) + \sin (- x) = - \csc (x)$
19417	Verify the Identity	cot(x)cos(x)=csc(x)-sin(x)	$\cot (x) \cos (x) = \csc (x) - \sin (x)$
19418	Verify the Identity	cot(x)csc(x)tan(x)^2=sec(x)	$\cot (x) \csc (x) \tan^{2} (x) = \sec (x)$
19419	Verify the Identity	cot(x)=- square root of 3	$\cot (x) = - \sqrt{3}$
19420	Verify the Identity	cot(x)=-cot(x)	$\cot (x) = - \cot (x)$
19421	Verify the Identity	cot(x)=-5/2	$\cot (x) = - \frac{5}{2}$
19422	Verify the Identity	cot(t)+(sin(t))/(1+cos(t))=csc(t)	$\cot (t) + \frac{\sin (t)}{1 + \cos (t)} = \csc (t)$
19423	Verify the Identity	cot(A+b)=(cot(a)cot(B)-1)/(cot(A)+cot(B))	$\cot (A + b) = \frac{\cot (a) \cot (B) - 1}{\cot (A) + \cot (B)}$
19424	Verify the Identity	cot(t)-sin(2t)=cot(t)cos(2t)	$\cot (t) - \sin (2 t) = \cot (t) \cos (2 t)$
19425	Verify the Identity	cot(x)(tan(x)+cot(x))=csc(x)^2	$\cot (x) (\tan (x) + \cot (x)) = \csc^{2} (x)$
19426	Verify the Identity	6arccos(2x)=5pi	$6 \arccos (2 x) = 5 π$
19427	Verify the Identity	8csc(x)^2-3cot(x)^2=3+5csc(x)^2	$8 \csc^{2} (x) - 3 \cot^{2} (x) = 3 + 5 \csc^{2} (x)$
19428	Verify the Identity	9sec(x)^2-5tan(x)^2=5+4sec(x)^2	$9 \sec^{2} (x) - 5 \tan^{2} (x) = 5 + 4 \sec^{2} (x)$
19429	Verify the Identity	5cos(2x)=-5cos(x)	$5 \cos (2 x) = - 5 \cos (x)$
19430	Verify the Identity	6cot(y)^2(sec(y-1)^2)=6	$6 \cot^{2} (y) (\sec^{2} (y - 1)) = 6$
19431	Verify the Identity	6sin(2t)+9sin(t)=0	$6 \sin (2 t) + 9 \sin (t) = 0$
19432	Verify the Identity	-cos(x)+cos(2x)=0	$- \cos (x) + \cos (2 x) = 0$
19433	Verify the Identity	cos(x)=1/(sec(x))	$\cos (x) = \frac{1}{\sec (x)}$
19434	Verify the Identity	cos(x)+sin(x)=0	$\cos (x) + \sin (x) = 0$
19435	Verify the Identity	arcsin(x)+arctan(x)=0	$\arcsin (x) + \arctan (x) = 0$
19436	Verify the Identity	arcsin(x)-arctan(( square root of 3)/3)=-pi/3	$\arcsin (x) - \arctan (\frac{\sqrt{3}}{3}) = - \frac{π}{3}$
19437	Verify the Identity	8sec(x)sin(x)=8cot(x)tan(x)^2	$8 \sec (x) \sin (x) = 8 \cot (x) \tan^{2} (x)$
19438	Verify the Identity	86.6=120 square root of 1-x/pi+(sin(2x))/(2pi)	$86.6 = 120 \sqrt{1 - \frac{x}{π} + \frac{\sin (2 x)}{2 π}}$
19439	Verify the Identity	arccsc(x)=arccos(1/x)	$arccsc (x) = \arccos (\frac{1}{x})$
19440	Verify the Identity	arccsc(x)=arcsin(1/x)	$arccsc (x) = \arcsin (\frac{1}{x})$
19441	Verify the Identity	arcsin(5/13)+arccos(x)=pi/4	$\arcsin (\frac{5}{13}) + \arccos (x) = \frac{π}{4}$
19442	Verify the Identity	4cos(x)^2=5-4sin(x)	$4 \cos^{2} (x) = 5 - 4 \sin (x)$
19443	Verify the Identity	3sin(x)=cos(x)	$3 \sin (x) = \cos (x)$
19444	Verify the Identity	3sin(a)cos(a)=sin(a)cos(a)+sin(2a)	$3 \sin (a) \cos (a) = \sin (a) \cos (a) + \sin (2 a)$
19445	Verify the Identity	4sin(x)^2=4cos(x+1)	$4 \sin^{2} (x) = 4 \cos (x + 1)$
19446	Verify the Identity	4sin(x)- square root of 3=2sin(x)	$4 \sin (x) - \sqrt{3} = 2 \sin (x)$
19447	Verify the Identity	4sin(x/2)=-4cos(x/2)	$4 \sin (\frac{x}{2}) = - 4 \cos (\frac{x}{2})$
19448	Verify the Identity	4cos(x)^4-1=0	$4 \cos^{4} (x) - 1 = 0$
19449	Verify the Identity	4sin(x)^2+2cos(x)^2=4-2cos(x)^2	$4 \sin^{2} (x) + 2 \cos^{2} (x) = 4 - 2 \cos^{2} (x)$
19450	Verify the Identity	4cos(x)=3sec(x)	$4 \cos (x) = 3 \sec (x)$
19451	Verify the Identity	3arccos(2x)=2pi	$3 \arccos (2 x) = 2 π$
19452	Verify the Identity	3cos(x)^2=sin(x)^2	$3 \cos^{2} (x) = \sin^{2} (x)$
19453	Verify the Identity	3sin(x)^2+4cos(x)^2=3+cos(x)^2	$3 \sin^{2} (x) + 4 \cos^{2} (x) = 3 + \cos^{2} (x)$
19454	Verify the Identity	4tan(x/4)=sin(x)sec(x/2)sec(x/4)sec(x/4)	$4 \tan (\frac{x}{4}) = \sin (x) \sec (\frac{x}{2}) \sec (\frac{x}{4}) \sec (\frac{x}{4})$
19455	Verify the Identity	3cos(x+y)+3cos(x-y)=6cos(x)cos(y)	$3 \cos (x + y) + 3 \cos (x - y) = 6 \cos (x) \cos (y)$
19456	Verify the Identity	3cos(2t)-5cos(t)-1=0	$3 \cos (2 t) - 5 \cos (t) - 1 = 0$
19457	Verify the Identity	3cos(x)+4sin(x)=5	$3 \cos (x) + 4 \sin (x) = 5$
19458	Verify the Identity	2tan(x)-2=0	$2 \tan (x) - 2 = 0$
19459	Verify the Identity	2tan(x)+2=0	$2 \tan (x) + 2 = 0$
19460	Verify the Identity	2sin(x)=1	$2 \sin (x) = 1$
19461	Verify the Identity	2sin(x)=sin(x)	$2 \sin (x) = \sin (x)$
19462	Verify the Identity	2sin(x)-1=0	$2 \sin (x) - 1 = 0$
19463	Verify the Identity	2cos(x)-3sin(x)=2.5	$2 \cos (x) - 3 \sin (x) = 2.5$
19464	Verify the Identity	2sin(2x)=-tan(2x)	$2 \sin (2 x) = - \tan (2 x)$
19465	Verify the Identity	2sin(5x)cos(x)=sin(6x)+sin(4x)	$2 \sin (5 x) \cos (x) = \sin (6 x) + \sin (4 x)$
19466	Verify the Identity	2sin(2x)+cos(x)=0	$2 \sin (2 x) + \cos (x) = 0$
19467	Verify the Identity	2sin(x)- square root of 2=0	$2 \sin (x) - \sqrt{2} = 0$
19468	Verify the Identity	2cos(x)-1=0	$2 \cos (x) - 1 = 0$
19469	Verify the Identity	2cos(x)-1=sec(x)	$2 \cos (x) - 1 = \sec (x)$
19470	Verify the Identity	2cos(x)cos(y)=cos(x+y)+cos(x-y)	$2 \cos (x) \cos (y) = \cos (x + y) + \cos (x - y)$
19471	Verify the Identity	2sin(x)^2+3sin(x)=-1	$2 \sin^{2} (x) + 3 \sin (x) = - 1$
19472	Verify the Identity	2sin(x)^2+5cos(x)+1=0	$2 \sin^{2} (x) + 5 \cos (x) + 1 = 0$
19473	Verify the Identity	2cos(x)^2-1=0	$2 \cos^{2} (x) - 1 = 0$
19474	Verify the Identity	2cos(x)^2-1=1-2sin(x)^2	$2 \cos^{2} (x) - 1 = 1 - 2 \sin^{2} (x)$
19475	Verify the Identity	2csc(x)^2=1/(1-cos(x))+1/(1+cos(x))	$2 \csc^{2} (x) = \frac{1}{1 - \cos (x)} + \frac{1}{1 + \cos (x)}$
19476	Verify the Identity	2-csc(x)^2=1-cot(x)^2	$2 - \csc^{2} (x) = 1 - \cot^{2} (x)$
19477	Verify the Identity	2*cos(arcsin(x)) = square root of 4-4x^2	$2 \cdot \cos (\arcsin (x)) = \sqrt{4 - 4 x^{2}}$
19478	Verify the Identity	-15cos(x)=-5sec(x)-10	$- 15 \cos (x) = - 5 \sec (x) - 10$
19479	Verify the Identity	1-cos(x) = square root of ((1-cos(x))^2)/(1-cos(x)^2)	$1 - \cos (x) = \sqrt{\frac{{(1 - \cos (x))}^{2}}{1 - \cos^{2} (x)}}$
19480	Verify the Identity	1-sec(x)cos(x)^3=sin(x)^2	$1 - \sec (x) \cos^{3} (x) = \sin^{2} (x)$
19481	Verify the Identity	1sin(30)=1.505sin(x)	$1 \sin (30) = 1.505 \sin (x)$
19482	Verify the Identity	1-sin(x)=cos(x)	$1 - \sin (x) = \cos (x)$
19483	Verify the Identity	(csc(x)^2)/(1+tan(x)^2)=cot(x)^2	$\frac{\csc^{2} (x)}{1 + \tan^{2} (x)} = \cot^{2} (x)$
19484	Verify the Identity	(sec(x)^4-tan(x)^4)/(sec(x)^2+tan(x)^2)=sec(x)^2-tan(x)^2	$\frac{\sec^{4} (x) - \tan^{4} (x)}{\sec^{2} (x) + \tan^{2} (x)} = \sec^{2} (x) - \tan^{2} (x)$
19485	Verify the Identity	sin(x)^2(x)=((sec(x)^2(x)-1)(1-sin(x)^4x))/(1+sin(x)^2(x))	$\sin^{2} (x) (x) = \frac{(\sec^{2} (x) (x) - 1) (1 - \sin^{4} (x) x)}{1 + \sin^{2} (x) (x)}$
19486	Verify the Identity	(csc(x)^2-1)/(csc(x)^2)=cos(x)^2	$\frac{\csc^{2} (x) - 1}{\csc^{2} (x)} = \cos^{2} (x)$
19487	Verify the Identity	(csc(x)^2)/(cot(x)^2-1)=(sec(x)^2)/(1-tan(x)^2)	$\frac{\csc^{2} (x)}{\cot^{2} (x) - 1} = \frac{\sec^{2} (x)}{1 - \tan^{2} (x)}$
19488	Verify the Identity	(sin(x)^2+2cos(x)-1)/(sin(x)^2+3cos(x)-3)=1/(1-sec(x))	$\frac{\sin^{2} (x) + 2 \cos (x) - 1}{\sin^{2} (x) + 3 \cos (x) - 3} = \frac{1}{1 - \sec (x)}$
19489	Verify the Identity	sin(x)^4-tan(x)^4=1+2*tan(x)^2	$\sin^{4} (x) - \tan^{4} (x) = 1 + 2 \cdot \tan^{2} (x)$
19490	Verify the Identity	(sin(theta)^2-tan(theta))/(cos(theta)^2-cot(theta))=tan(theta)^2	$\frac{\sin^{2} (θ) - \tan (θ)}{\cos^{2} (θ) - \cot (θ)} = \tan^{2} (θ)$
19491	Verify the Identity	(sin(x)^2)/(cos(x))=sec(x)-cos(x)	$\frac{\sin^{2} (x)}{\cos (x)} = \sec (x) - \cos (x)$
19492	Verify the Identity	(sin(x)^2-tan(x))/(cos(x)^2-cot(x))=tan(x)^2	$\frac{\sin^{2} (x) - \tan (x)}{\cos^{2} (x) - \cot (x)} = \tan^{2} (x)$
19493	Verify the Identity	(1-tan(x)^2)/(1+tan(x)^2)=cos(x)^2-sin(x)^2	$\frac{1 - \tan^{2} (x)}{1 + \tan^{2} (x)} = \cos^{2} (x) - \sin^{2} (x)$
19494	Verify the Identity	(1-tan(x)^4)/(sec(x)^2)=1-tan(x)^2	$\frac{1 - \tan^{4} (x)}{\sec^{2} (x)} = 1 - \tan^{2} (x)$
19495	Verify the Identity	(tan(x)^2)/(sec(x))=sin(x)tan(x)	$\frac{\tan^{2} (x)}{\sec (x)} = \sin (x) \tan (x)$
19496	Verify the Identity	(sin(x)^3+cos(x)^3)/(1-2cos(x)^2)=(sec(x)-sin(x))/(tan(x)-1)	$\frac{\sin^{3} (x) + \cos^{3} (x)}{1 - 2 \cos^{2} (x)} = \frac{\sec (x) - \sin (x)}{\tan (x) - 1}$
19497	Verify the Identity	(cos(x)^2)/(1+sin(x))=1-sin(x)	$\frac{\cos^{2} (x)}{1 + \sin (x)} = 1 - \sin (x)$
19498	Verify the Identity	(cos(x)^2-sin(x)^2)/(1-tan(x)^2)=cos(x)^2	$\frac{\cos^{2} (x) - \sin^{2} (x)}{1 - \tan^{2} (x)} = \cos^{2} (x)$
19499	Verify the Identity	(1/(sin(x))+1)/(1/(sin(x))-1)=tan(x)^2+2tan(x)sec(x)+sec(x)^2	$\frac{\frac{1}{\sin (x)} + 1}{\frac{1}{\sin (x)} - 1} = \tan^{2} (x) + 2 \tan (x) \sec (x) + \sec^{2} (x)$
19500	Verify the Identity	(tan(theta)^2(theta))/(sec(theta))=sin(theta)tan(theta)	$\frac{\tan^{2} (θ) (θ)}{\sec (θ)} = \sin (θ) \tan (θ)$