We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

en

English

Upgrade

Popular Problems

Topics

Popular Trigonometry Problems

prove sin(θ)cos(θ)=tan(θ)	prove\:\sin(θ)\cos(θ)=\tan(θ)
prove sin(θ)cos(θ)=cot(θ)	prove\:\sin(θ)\cos(θ)=\cot(θ)
prove 1+(cos^2(x))/(sin(x)-1)=-sin(x)	prove\:1+\frac{\cos^{2}(x)}{\sin(x)-1}=-\sin(x)
prove sin(3x)=3cos^2(x)sin(x)-sin^3(x)	prove\:\sin(3x)=3\cos^{2}(x)\sin(x)-\sin^{3}(x)
prove 1-2sin^2(x)=cos^2(x)-sin^2(x)	prove\:1-2\sin^{2}(x)=\cos^{2}(x)-\sin^{2}(x)
prove cos(3x)+cos(x)=4cos^3(x)-2cos(x)	prove\:\cos(3x)+\cos(x)=4\cos^{3}(x)-2\cos(x)
prove (cos(x))/(sin(x))=cot(x)	prove\:\frac{\cos(x)}{\sin(x)}=\cot(x)
prove 3sin(x)-4sin^3(x)=sin(3x)	prove\:3\sin(x)-4\sin^{3}(x)=\sin(3x)
prove cos(2x)-3sin^2(x)=1-5sin^2(x)	prove\:\cos(2x)-3\sin^{2}(x)=1-5\sin^{2}(x)
prove (1-sin(x))/(1-1/(sin(x)))=-sin(x)	prove\:\frac{1-\sin(x)}{1-\frac{1}{\sin(x)}}=-\sin(x)
prove cos(x)=cos^3(x)+cos(x)sin^2(x)	prove\:\cos(x)=\cos^{3}(x)+\cos(x)\sin^{2}(x)
prove (cos(t))/(1+sin(t))+(1-sin(t))/(cos(t))=2(sec(t)-tan(t))	prove\:\frac{\cos(t)}{1+\sin(t)}+\frac{1-\sin(t)}{\cos(t)}=2(\sec(t)-\tan(t))
prove csc(x)-sin(x)=(cot^2(x))/(csc(x))	prove\:\csc(x)-\sin(x)=\frac{\cot^{2}(x)}{\csc(x)}
prove (cot(2θ))/(cos(2θ))=csc(2θ)	prove\:\frac{\cot(2θ)}{\cos(2θ)}=\csc(2θ)
prove (1+tan^2(x))sin^2(x)=tan^2(x)	prove\:(1+\tan^{2}(x))\sin^{2}(x)=\tan^{2}(x)
prove sec^2(x)=(sec(x))^2	prove\:\sec^{2}(x)=(\sec(x))^{2}
prove sin(2x)(cot(x)+tan(x))=2	prove\:\sin(2x)(\cot(x)+\tan(x))=2
prove tan(x/2)csc(x)= 1/(1+cos(x))	prove\:\tan(\frac{x}{2})\csc(x)=\frac{1}{1+\cos(x)}
prove csc^4(x)cot(x)=csc^2(x)(cot(x)+cot^3(x))	prove\:\csc^{4}(x)\cot(x)=\csc^{2}(x)(\cot(x)+\cot^{3}(x))
prove cos^3(θ)+cos(θ)sin^2(θ)=cos(θ)	prove\:\cos^{3}(θ)+\cos(θ)\sin^{2}(θ)=\cos(θ)
prove csc(θ)sin(θ)=1	prove\:\csc(θ)\sin(θ)=1
prove (cos(x)-cos(9x))/(sin(x)+sin(9x))=tan(4x)	prove\:\frac{\cos(x)-\cos(9x)}{\sin(x)+\sin(9x)}=\tan(4x)
prove (2-sec^2(x))/(sec^2(x)+2tan(x))=(cos(x)-sin(x))/(cos(x)+sin(x))	prove\:\frac{2-\sec^{2}(x)}{\sec^{2}(x)+2\tan(x)}=\frac{\cos(x)-\sin(x)}{\cos(x)+\sin(x)}
prove (1-cos(x))^2=csc^2(x)-2cot(x)	prove\:(1-\cos(x))^{2}=\csc^{2}(x)-2\cot(x)
prove cos^2(9x)-sin^2(9x)=cos(18x)	prove\:\cos^{2}(9x)-\sin^{2}(9x)=\cos(18x)
prove 1+cot^2(30)=csc^2(30)	prove\:1+\cot^{2}(30^{\circ\:})=\csc^{2}(30^{\circ\:})
prove 1/(1+tan^2(θ))=cos^2(θ)	prove\:\frac{1}{1+\tan^{2}(θ)}=\cos^{2}(θ)
prove cos(2x)=cos^2(x)	prove\:\cos(2x)=\cos^{2}(x)
prove sin^2(x)-1=cos^2(x)	prove\:\sin^{2}(x)-1=\cos^{2}(x)
prove tan(pi/4-t)=(1-tan(t))/(1+tan(t))	prove\:\tan(\frac{π}{4}-t)=\frac{1-\tan(t)}{1+\tan(t)}
prove-tan(x)=tan(-x)	prove\:-\tan(x)=\tan(-x)
prove (csc(θ)+sin(θ))/(tan(θ)+1)=csc(θ)	prove\:\frac{\csc(θ)+\sin(θ)}{\tan(θ)+1}=\csc(θ)
prove-sin^2(x)-cos^2(x)=-1	prove\:-\sin^{2}(x)-\cos^{2}(x)=-1
prove sin(3θ)=3cos^2(θ)sin(θ)-sin^3(θ)	prove\:\sin(3θ)=3\cos^{2}(θ)\sin(θ)-\sin^{3}(θ)
prove (tan(θ)cos(θ))/(sin(θ))=1	prove\:\frac{\tan(θ)\cos(θ)}{\sin(θ)}=1
prove 2sin^2(x/2)+cos(x)=1	prove\:2\sin^{2}(\frac{x}{2})+\cos(x)=1
prove sec(x)-cos(x)=sin(x)(tan(x))	prove\:\sec(x)-\cos(x)=\sin(x)(\tan(x))
prove sin(x)sin(3x)=4sin(x)cos^2(x)	prove\:\sin(x)\sin(3x)=4\sin(x)\cos^{2}(x)
prove sec(pi/2-t)=csc(t)	prove\:\sec(\frac{π}{2}-t)=\csc(t)
prove-sin(2θ)=(-2cot(θ))/(1+cot^2(θ))	prove\:-\sin(2θ)=\frac{-2\cot(θ)}{1+\cot^{2}(θ)}
prove csc(x)sec(x)=tan(x)+cot(x)	prove\:\csc(x)\sec(x)=\tan(x)+\cot(x)
prove cot^2(x/2)=(sec(x)+1)/(sec(x)-1)	prove\:\cot^{2}(\frac{x}{2})=\frac{\sec(x)+1}{\sec(x)-1}
prove sin(3u)=sin(u)(3-4sin^2(u))	prove\:\sin(3u)=\sin(u)(3-4\sin^{2}(u))
prove 2cos^2(x/2)=1+cos(x)	prove\:2\cos^{2}(\frac{x}{2})=1+\cos(x)
prove tan(a)+(cos(a))/(1+sin(a))=sec(a)	prove\:\tan(a)+\frac{\cos(a)}{1+\sin(a)}=\sec(a)
prove (cos^2(A))/(cos(A)-sin(A))+(sin(A))/(1-cot(A))=sin(A)+cos(A)	prove\:\frac{\cos^{2}(A)}{\cos(A)-\sin(A)}+\frac{\sin(A)}{1-\cot(A)}=\sin(A)+\cos(A)
prove sec(a)+tan(a)=(cos(a))/(1-sin(a))	prove\:\sec(a)+\tan(a)=\frac{\cos(a)}{1-\sin(a)}
prove cos(x-pi/6)-sin(x+pi/3)=0	prove\:\cos(x-\frac{π}{6})-\sin(x+\frac{π}{3})=0
prove cot^2(α)+1= 1/(sin^2(α))	prove\:\cot^{2}(α)+1=\frac{1}{\sin^{2}(α)}
prove sin(3x)=3sin(x)cos^2(x)-sin^3(x)	prove\:\sin(3x)=3\sin(x)\cos^{2}(x)-\sin^{3}(x)
prove (cot(x)+tan(x))/(sec(x))=csc(x)	prove\:\frac{\cot(x)+\tan(x)}{\sec(x)}=\csc(x)
prove (cos(3x)-cos(5x))/(sin(3x)+sin(5x))=tan(x)	prove\:\frac{\cos(3x)-\cos(5x)}{\sin(3x)+\sin(5x)}=\tan(x)
prove (1+tan^2(x))cos^2(x)=1	prove\:(1+\tan^{2}(x))\cos^{2}(x)=1
prove (1-sin(θ))/(cos(θ))=sec(θ)-tan(θ)	prove\:\frac{1-\sin(θ)}{\cos(θ)}=\sec(θ)-\tan(θ)
prove cos^2(x)= 1/2+1/2 cos(2x)	prove\:\cos^{2}(x)=\frac{1}{2}+\frac{1}{2}\cos(2x)
prove tan(θ/2)=(1-cos(θ))/(sin(θ))	prove\:\tan(\frac{θ}{2})=\frac{1-\cos(θ)}{\sin(θ)}
prove cot(1/x)=(cos(1/x))/(sin(1/x))	prove\:\cot(\frac{1}{x})=\frac{\cos(\frac{1}{x})}{\sin(\frac{1}{x})}
prove (1+cos(4x))/2 =cos^2(2x)	prove\:\frac{1+\cos(4x)}{2}=\cos^{2}(2x)
prove 1/(2cos(x)sin(x))=csc(2x)	prove\:\frac{1}{2\cos(x)\sin(x)}=\csc(2x)
prove cos(x+pi/2)=sin(x)	prove\:\cos(x+\frac{π}{2})=\sin(x)
prove (sec(x)-cos(x))/(cos(x))=tan^2(x)	prove\:\frac{\sec(x)-\cos(x)}{\cos(x)}=\tan^{2}(x)
prove 1-cos^4(x)=2sin^2(x)-sin^4(x)	prove\:1-\cos^{4}(x)=2\sin^{2}(x)-\sin^{4}(x)
prove tan(pi/2-x)sin(x)=cos(x)	prove\:\tan(\frac{π}{2}-x)\sin(x)=\cos(x)
prove (1+sin(x))(1+sin(-x))=cos^2(x)	prove\:(1+\sin(x))(1+\sin(-x))=\cos^{2}(x)
prove 1-tan^2(x/2)=(2cos(x))/(1+cos(x))	prove\:1-\tan^{2}(\frac{x}{2})=\frac{2\cos(x)}{1+\cos(x)}
prove (1+cos(θ))/(1+sec(θ))=cos(θ)	prove\:\frac{1+\cos(θ)}{1+\sec(θ)}=\cos(θ)
prove tan^2(θ)-sec^2(θ)=-1	prove\:\tan^{2}(θ)-\sec^{2}(θ)=-1
prove cot(x)sin(x)-cos^2(x)sec(x)=0	prove\:\cot(x)\sin(x)-\cos^{2}(x)\sec(x)=0
prove (cos(3x))/(cos(x))=4cos^2(x)-3	prove\:\frac{\cos(3x)}{\cos(x)}=4\cos^{2}(x)-3
prove (1-cos(2θ))/2 =sin^2(θ)	prove\:\frac{1-\cos(2θ)}{2}=\sin^{2}(θ)
prove (sec(θ)+tan(θ))(1-sin(θ))=cos(θ)	prove\:(\sec(θ)+\tan(θ))(1-\sin(θ))=\cos(θ)
prove (csc^4(x)-1)/(cot^2(x))=2+cot^2(x)	prove\:\frac{\csc^{4}(x)-1}{\cot^{2}(x)}=2+\cot^{2}(x)
prove sin(arcsin(x)+arccos(x))=1	prove\:\sin(\arcsin(x)+\arccos(x))=1
prove (1-2sec(x)-3sec^2(x))/(-tan^2(x))=(1-3sec(x))/(1-sec(x))	prove\:\frac{1-2\sec(x)-3\sec^{2}(x)}{-\tan^{2}(x)}=\frac{1-3\sec(x)}{1-\sec(x)}
prove 1/(2csc(2x))=cos^2(x)tan(x)	prove\:\frac{1}{2\csc(2x)}=\cos^{2}(x)\tan(x)
prove (sec(5x)-1)(sec(5x)-1)=tan^2(5x)	prove\:(\sec(5x)-1)(\sec(5x)-1)=\tan^{2}(5x)
prove 1-cos(x)sin(x)cot(x)=sin^2(x)	prove\:1-\cos(x)\sin(x)\cot(x)=\sin^{2}(x)
prove cot(x)+tan(x)=sec(x)*csc(x)	prove\:\cot(x)+\tan(x)=\sec(x)\cdot\:\csc(x)
prove cot(4x)=(1-tan^2(2x))/(2tan(2x))	prove\:\cot(4x)=\frac{1-\tan^{2}(2x)}{2\tan(2x)}
prove sin(16x)=2sin(8x)cos(8x)	prove\:\sin(16x)=2\sin(8x)\cos(8x)
prove-cos(2θ)=(1-cot^2(θ))/(1+cot^2(θ))	prove\:-\cos(2θ)=\frac{1-\cot^{2}(θ)}{1+\cot^{2}(θ)}
prove sin(pi/2-x)sec(x)=1	prove\:\sin(\frac{π}{2}-x)\sec(x)=1
prove (sin(θ))/(1-cos^2(θ))=csc(θ)	prove\:\frac{\sin(θ)}{1-\cos^{2}(θ)}=\csc(θ)
prove sin(a)sec(a)=tan(a)	prove\:\sin(a)\sec(a)=\tan(a)
prove cos(x)(tan^2(+1))=sec(x)	prove\:\cos(x)(\tan^{2}(+1))=\sec(x)
prove cos^2(θ)+cos^2(θ)cot^2(θ)=cot^2(θ)	prove\:\cos^{2}(θ)+\cos^{2}(θ)\cot^{2}(θ)=\cot^{2}(θ)
prove cot^2(x)=csc^2(x)-csc^2(x)sin^2(x)	prove\:\cot^{2}(x)=\csc^{2}(x)-\csc^{2}(x)\sin^{2}(x)
prove (1-tan^2(θ))/(1+tan^2(θ))=cos(2θ)	prove\:\frac{1-\tan^{2}(θ)}{1+\tan^{2}(θ)}=\cos(2θ)
prove (tan^2(x))/(sin^2(x))=1+tan^2(x)	prove\:\frac{\tan^{2}(x)}{\sin^{2}(x)}=1+\tan^{2}(x)
prove sin^2(x)+cos^2(x)=cos(x)sec(x)	prove\:\sin^{2}(x)+\cos^{2}(x)=\cos(x)\sec(x)
prove sec(y)+tan(y)=(cos(y))/(1-sin(y))	prove\:\sec(y)+\tan(y)=\frac{\cos(y)}{1-\sin(y)}
prove (csc(x)+cot(x))(sec(x)-1)=tan(x)	prove\:(\csc(x)+\cot(x))(\sec(x)-1)=\tan(x)
prove cos(x-pi/2)=cos(x)tan(x)	prove\:\cos(x-\frac{π}{2})=\cos(x)\tan(x)
prove csc(-θ)=-csc(θ)	prove\:\csc(-θ)=-\csc(θ)
prove cot^2(x)sin^2(x)=cos^2(x)	prove\:\cot^{2}(x)\sin^{2}(x)=\cos^{2}(x)
prove (cos(θ))/(tan(θ)+sec(θ))=1-sin(θ)	prove\:\frac{\cos(θ)}{\tan(θ)+\sec(θ)}=1-\sin(θ)
prove sec(x)-tan(x)(sin(x))= 1/(sec(x))	prove\:\sec(x)-\tan(x)(\sin(x))=\frac{1}{\sec(x)}
prove sin^2(x)+2cos^2(x)-1=cos^2(x)	prove\:\sin^{2}(x)+2\cos^{2}(x)-1=\cos^{2}(x)
prove (1-tan^4(x))/(sec^2(x))=1-tan^2(x)	prove\:\frac{1-\tan^{4}(x)}{\sec^{2}(x)}=1-\tan^{2}(x)
prove tan^2(x)=sec(x)csc(x)tan(x)-1	prove\:\tan^{2}(x)=\sec(x)\csc(x)\tan(x)-1

1
..
223
224
225
226
227
..
451