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Popular Trigonometry Problems

prove (sin(x))/(1-cos(x))-cot(x)=csc(x)	prove\:\frac{\sin(x)}{1-\cos(x)}-\cot(x)=\csc(x)
prove (1-tan(x))^2=sec^2(x)-2tan(x)	prove\:(1-\tan(x))^{2}=\sec^{2}(x)-2\tan(x)
prove sec(x)-sec(x)sin^2(x)=cos(x)	prove\:\sec(x)-\sec(x)\sin^{2}(x)=\cos(x)
prove sin(2x)=2sin(x)cos(x)	prove\:\sin(2x)=2\sin(x)\cos(x)
prove (csc^2(x))/(cot(x))=csc(x)sec(x)	prove\:\frac{\csc^{2}(x)}{\cot(x)}=\csc(x)\sec(x)
prove sec(x)+tan(x)=(cos(x))/(1-sin(x))	prove\:\sec(x)+\tan(x)=\frac{\cos(x)}{1-\sin(x)}
prove csc(x)-cot(x)cos(x)=sin(x)	prove\:\csc(x)-\cot(x)\cos(x)=\sin(x)
prove cos(2x)=1-2sin^2(x)	prove\:\cos(2x)=1-2\sin^{2}(x)
prove tan(x)=(sin(x))/(cos(x))	prove\:\tan(x)=\frac{\sin(x)}{\cos(x)}
prove (tan^2(x))/(sec(x))=sec(x)-cos(x)	prove\:\frac{\tan^{2}(x)}{\sec(x)}=\sec(x)-\cos(x)
prove (sin(x)+cos(x))^2=1+2sin(x)cos(x)	prove\:(\sin(x)+\cos(x))^{2}=1+2\sin(x)\cos(x)
prove sin(θ)sec(θ)=tan(θ)	prove\:\sin(θ)\sec(θ)=\tan(θ)
prove csc(x)-sin(x)=cos(x)cot(x)	prove\:\csc(x)-\sin(x)=\cos(x)\cot(x)
prove cos^2(θ)(1+tan^2(θ))=1	prove\:\cos^{2}(θ)(1+\tan^{2}(θ))=1
prove (cot^2(x))/(csc(x))=csc(x)-sin(x)	prove\:\frac{\cot^{2}(x)}{\csc(x)}=\csc(x)-\sin(x)
prove tanh(x)=(sinh(x))/(cosh(x))	prove\:\tanh(x)=\frac{\sinh(x)}{\cosh(x)}
prove (cos(x))/(1+sin(x))=sec(x)-tan(x)	prove\:\frac{\cos(x)}{1+\sin(x)}=\sec(x)-\tan(x)
prove cot(x)+tan(x)=(sec(x))(csc(x))	prove\:\cot(x)+\tan(x)=(\sec(x))(\csc(x))
prove sin(x)sec(x)=tan(x)	prove\:\sin(x)\sec(x)=\tan(x)
prove cos(4x)=8cos^4(x)-8cos^2(x)+1	prove\:\cos(4x)=8\cos^{4}(x)-8\cos^{2}(x)+1
prove tan(x)+(cos(x))/(1+sin(x))=sec(x)	prove\:\tan(x)+\frac{\cos(x)}{1+\sin(x)}=\sec(x)
prove tan(x)+cot(x)=csc(x)sec(x)	prove\:\tan(x)+\cot(x)=\csc(x)\sec(x)
prove (csc(x))/(cot(x)+tan(x))=cos(x)	prove\:\frac{\csc(x)}{\cot(x)+\tan(x)}=\cos(x)
prove (sec(x)-cos(x))/(sec(x))=sin^2(x)	prove\:\frac{\sec(x)-\cos(x)}{\sec(x)}=\sin^{2}(x)
prove tan^2(θ)-sin^2(θ)=tan^2(θ)sin^2(θ)	prove\:\tan^{2}(θ)-\sin^{2}(θ)=\tan^{2}(θ)\sin^{2}(θ)
prove sin^2(x)(1+cot^2(x))=1	prove\:\sin^{2}(x)(1+\cot^{2}(x))=1
prove sin(θ)(cot(θ)+tan(θ))=sec(θ)	prove\:\sin(θ)(\cot(θ)+\tan(θ))=\sec(θ)
prove cos^2(x)+sin^2(x)=1	prove\:\cos^{2}(x)+\sin^{2}(x)=1
prove cos(2x)=2cos^2(x)-1	prove\:\cos(2x)=2\cos^{2}(x)-1
prove tan(θ)sin(θ)+cos(θ)=sec(θ)	prove\:\tan(θ)\sin(θ)+\cos(θ)=\sec(θ)
prove sin(3x)=3sin(x)-4sin^3(x)	prove\:\sin(3x)=3\sin(x)-4\sin^{3}(x)
prove cos(θ)(tan(θ)+cot(θ))=csc(θ)	prove\:\cos(θ)(\tan(θ)+\cot(θ))=\csc(θ)
prove csc(x)-csc(x)cos^2(x)=sin(x)	prove\:\csc(x)-\csc(x)\cos^{2}(x)=\sin(x)
prove sec^2(x)cot(x)-cot(x)=tan(x)	prove\:\sec^{2}(x)\cot(x)-\cot(x)=\tan(x)
prove tan(x)sin(x)+cos(x)=sec(x)	prove\:\tan(x)\sin(x)+\cos(x)=\sec(x)
prove cos^2(x)(1+tan^2(x))=1	prove\:\cos^{2}(x)(1+\tan^{2}(x))=1
prove (1+cos(x))/(sin(x))=csc(x)+cot(x)	prove\:\frac{1+\cos(x)}{\sin(x)}=\csc(x)+\cot(x)
prove (sin(2x))/(1-cos(2x))=cot(x)	prove\:\frac{\sin(2x)}{1-\cos(2x)}=\cot(x)
prove (tan(x))/(sec(x))=sin(x)	prove\:\frac{\tan(x)}{\sec(x)}=\sin(x)
prove sin^2(θ)+cos^2(θ)=1	prove\:\sin^{2}(θ)+\cos^{2}(θ)=1
prove sec(θ)-cos(θ)=sin(θ)tan(θ)	prove\:\sec(θ)-\cos(θ)=\sin(θ)\tan(θ)
prove sin(x-pi/2)=-cos(x)	prove\:\sin(x-\frac{π}{2})=-\cos(x)
prove sin^2(x)-cos^2(x)=1-2cos^2(x)	prove\:\sin^{2}(x)-\cos^{2}(x)=1-2\cos^{2}(x)
prove cos(x)tan(x)=sin(x)	prove\:\cos(x)\tan(x)=\sin(x)
prove cos^2(y)-sin^2(y)=1-2sin^2(y)	prove\:\cos^{2}(y)-\sin^{2}(y)=1-2\sin^{2}(y)
prove cos(x)-cos^3(x)=cos(x)sin^2(x)	prove\:\cos(x)-\cos^{3}(x)=\cos(x)\sin^{2}(x)
prove cos^4(x)-sin^4(x)=1-2sin^2(x)	prove\:\cos^{4}(x)-\sin^{4}(x)=1-2\sin^{2}(x)
prove sin(x+y)-sin(x-y)=2cos(x)sin(y)	prove\:\sin(x+y)-\sin(x-y)=2\cos(x)\sin(y)
prove csc^2(θ)tan^2(θ)-1=tan^2(θ)	prove\:\csc^{2}(θ)\tan^{2}(θ)-1=\tan^{2}(θ)
prove cot(2x)=(cot^2(x)-1)/(2cot(x))	prove\:\cot(2x)=\frac{\cot^{2}(x)-1}{2\cot(x)}
prove (1-sin^2(x))csc(x)=cos(x)cot(x)	prove\:(1-\sin^{2}(x))\csc(x)=\cos(x)\cot(x)
prove sin(x)+sin(x)cot^2(x)=csc(x)	prove\:\sin(x)+\sin(x)\cot^{2}(x)=\csc(x)
prove (sec^2(x))/(sec^2(x)-1)=csc^2(x)	prove\:\frac{\sec^{2}(x)}{\sec^{2}(x)-1}=\csc^{2}(x)
prove cot^2(x)-cos^2(x)=cos^2(x)cot^2(x)	prove\:\cot^{2}(x)-\cos^{2}(x)=\cos^{2}(x)\cot^{2}(x)
prove sin(pi/2+x)=cos(x)	prove\:\sin(\frac{π}{2}+x)=\cos(x)
prove sin^2(x)-cos^2(x)=2sin^2(x)-1	prove\:\sin^{2}(x)-\cos^{2}(x)=2\sin^{2}(x)-1
prove cos(x+y)+cos(x-y)=2cos(x)cos(y)	prove\:\cos(x+y)+\cos(x-y)=2\cos(x)\cos(y)
prove 1-(sin^2(x))/(1+cos(x))=cos(x)	prove\:1-\frac{\sin^{2}(x)}{1+\cos(x)}=\cos(x)
prove csc(x)-(sin(x))/(1+cos(x))=cot(x)	prove\:\csc(x)-\frac{\sin(x)}{1+\cos(x)}=\cot(x)
prove sin(2x)=(2tan(x))/(1+tan^2(x))	prove\:\sin(2x)=\frac{2\tan(x)}{1+\tan^{2}(x)}
prove (tan^2(x)+1)(cos^2(x)-1)=-tan^2(x)	prove\:(\tan^{2}(x)+1)(\cos^{2}(x)-1)=-\tan^{2}(x)
prove sec^2(θ)(1-sin^2(θ))=1	prove\:\sec^{2}(θ)(1-\sin^{2}(θ))=1
prove 1-(cos^2(θ))/(1+sin(θ))=sin(θ)	prove\:1-\frac{\cos^{2}(θ)}{1+\sin(θ)}=\sin(θ)
prove (sec(x)-1)/(1-cos(x))=sec(x)	prove\:\frac{\sec(x)-1}{1-\cos(x)}=\sec(x)
prove sin(x)tan(x)+cos(x)=sec(x)	prove\:\sin(x)\tan(x)+\cos(x)=\sec(x)
prove csc(θ)cos(θ)=cot(θ)	prove\:\csc(θ)\cos(θ)=\cot(θ)
prove csc^2(x)tan^2(x)-1=tan^2(x)	prove\:\csc^{2}(x)\tan^{2}(x)-1=\tan^{2}(x)
prove sin(x)-sin(x)cos^2(x)=sin^3(x)	prove\:\sin(x)-\sin(x)\cos^{2}(x)=\sin^{3}(x)
prove sec(x)= 1/(cos(x))	prove\:\sec(x)=\frac{1}{\cos(x)}
prove sin^2(x)= 1/2-1/2 cos(2x)	prove\:\sin^{2}(x)=\frac{1}{2}-\frac{1}{2}\cos(2x)
prove tan(x)+sec(x)=(cos(x))/(1-sin(x))	prove\:\tan(x)+\sec(x)=\frac{\cos(x)}{1-\sin(x)}
prove csc^2(x)-cot^2(x)=1	prove\:\csc^{2}(x)-\cot^{2}(x)=1
prove cot(x)-tan(x)=2cot(2x)	prove\:\cot(x)-\tan(x)=2\cot(2x)
prove 1-(cos^2(x))/(1+sin(x))=sin(x)	prove\:1-\frac{\cos^{2}(x)}{1+\sin(x)}=\sin(x)
prove tan^2(x)-sin^2(x)=sin^2(x)tan^2(x)	prove\:\tan^{2}(x)-\sin^{2}(x)=\sin^{2}(x)\tan^{2}(x)
prove sin^4(x)-cos^4(x)=2sin^2(x)-1	prove\:\sin^{4}(x)-\cos^{4}(x)=2\sin^{2}(x)-1
prove (sec(θ)-1)(sec(θ)+1)=tan^2(θ)	prove\:(\sec(θ)-1)(\sec(θ)+1)=\tan^{2}(θ)
prove 1+tan^2(x)=sec^2(x)	prove\:1+\tan^{2}(x)=\sec^{2}(x)
prove sin^3(2x)=(1/2 sin(2x))(1-cos(4x))	prove\:\sin^{3}(2x)=(\frac{1}{2}\sin(2x))(1-\cos(4x))
prove cos(θ)tan(θ)=sin(θ)	prove\:\cos(θ)\tan(θ)=\sin(θ)
prove (sin^2(x))/(1-cos(x))=1+cos(x)	prove\:\frac{\sin^{2}(x)}{1-\cos(x)}=1+\cos(x)
prove sin(x+y)+sin(x-y)=2sin(x)cos(y)	prove\:\sin(x+y)+\sin(x-y)=2\sin(x)\cos(y)
prove cos(2θ)=cos^2(θ)-sin^2(θ)	prove\:\cos(2θ)=\cos^{2}(θ)-\sin^{2}(θ)
prove sec(θ)-cos(θ)=tan(θ)sin(θ)	prove\:\sec(θ)-\cos(θ)=\tan(θ)\sin(θ)
prove (csc(θ)+sec(θ))/(tan(θ)+1)=csc(θ)	prove\:\frac{\csc(θ)+\sec(θ)}{\tan(θ)+1}=\csc(θ)
prove cot(x)cos(x)+sin(x)=csc(x)	prove\:\cot(x)\cos(x)+\sin(x)=\csc(x)
prove sin(3θ)=3sin(θ)-4sin^3(θ)	prove\:\sin(3θ)=3\sin(θ)-4\sin^{3}(θ)
prove sin^4(t)-cos^4(t)=1-2cos^2(t)	prove\:\sin^{4}(t)-\cos^{4}(t)=1-2\cos^{2}(t)
prove (1-cos^2(x))(1+cot^2(x))=1	prove\:(1-\cos^{2}(x))(1+\cot^{2}(x))=1
prove sin^2(x)=1-cos^2(x)	prove\:\sin^{2}(x)=1-\cos^{2}(x)
prove (1-cos(-x))/(sec(-x)-1)=cos(x)	prove\:\frac{1-\cos(-x)}{\sec(-x)-1}=\cos(x)
prove cos(3θ)=4cos^3(θ)-3cos(θ)	prove\:\cos(3θ)=4\cos^{3}(θ)-3\cos(θ)
prove (sin(x)-cos(x))^2=1-sin(2x)	prove\:(\sin(x)-\cos(x))^{2}=1-\sin(2x)
prove csc(θ)tan(θ)=sec(θ)	prove\:\csc(θ)\tan(θ)=\sec(θ)
prove (1+sin(-x))/(1+csc(-x))=-sin(x)	prove\:\frac{1+\sin(-x)}{1+\csc(-x)}=-\sin(x)
prove tan^2(x)+1=sec^2(x)	prove\:\tan^{2}(x)+1=\sec^{2}(x)
prove (1+csc(x))/(sec(x))=cos(x)+cot(x)	prove\:\frac{1+\csc(x)}{\sec(x)}=\cos(x)+\cot(x)
prove cos(-x)=cos(x)	prove\:\cos(-x)=\cos(x)
prove cos(pi+x)=-cos(x)	prove\:\cos(π+x)=-\cos(x)
prove (1-cos^2(x))sec(x)=sin(x)tan(x)	prove\:(1-\cos^{2}(x))\sec(x)=\sin(x)\tan(x)

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