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Popular Trigonometry Problems

prove 2cot(x)cot(2x)=cot^2(x)-1	prove\:2\cot(x)\cot(2x)=\cot^{2}(x)-1
prove sin(x)(sec(x)+csc(x))=tan(x)+1	prove\:\sin(x)(\sec(x)+\csc(x))=\tan(x)+1
prove 1-cot(x)=sqrt((csc^2(x)-2cot(x)))	prove\:1-\cot(x)=\sqrt{(\csc^{2}(x)-2\cot(x))}
prove cos^2(x)(tan^2(x)+1)=1	prove\:\cos^{2}(x)(\tan^{2}(x)+1)=1
prove cos(x)= 1/(sec(x))	prove\:\cos(x)=\frac{1}{\sec(x)}
prove 1-cos^2(θ)=sin(θ)cos(θ)tan(θ)	prove\:1-\cos^{2}(θ)=\sin(θ)\cos(θ)\tan(θ)
prove arctan(x)= 1/(tan(x))	prove\:\arctan(x)=\frac{1}{\tan(x)}
prove tan(θ/2)=csc(θ)-cot(θ)	prove\:\tan(\frac{θ}{2})=\csc(θ)-\cot(θ)
prove cos(4x)=1-8sin^2(x)+8sin^4(x)	prove\:\cos(4x)=1-8\sin^{2}(x)+8\sin^{4}(x)
prove (sin(θ)-cos(θ))^2=1-sin(2θ)	prove\:(\sin(θ)-\cos(θ))^{2}=1-\sin(2θ)
prove (sec(x))/(csc(x))=tan(x)	prove\:\frac{\sec(x)}{\csc(x)}=\tan(x)
prove (csc(x))/(sec(x))=cot(x)	prove\:\frac{\csc(x)}{\sec(x)}=\cot(x)
prove cot^2(θ)(1+tan^2(θ))=csc^2(θ)	prove\:\cot^{2}(θ)(1+\tan^{2}(θ))=\csc^{2}(θ)
prove sin(2A)=2sin(A)	prove\:\sin(2A)=2\sin(A)
prove tan(θ)cos(θ)csc(θ)=1	prove\:\tan(θ)\cos(θ)\csc(θ)=1
prove sin^2(x+pi/4)-cos^2(x-pi/4)=0	prove\:\sin^{2}(x+\frac{π}{4})-\cos^{2}(x-\frac{π}{4})=0
prove tan^2(u)-sin^2(u)=tan^2(u)sin^2(u)	prove\:\tan^{2}(u)-\sin^{2}(u)=\tan^{2}(u)\sin^{2}(u)
prove cos(x)-cos(x)sin^2(x)=cos^3(x)	prove\:\cos(x)-\cos(x)\sin^{2}(x)=\cos^{3}(x)
prove sin^2(x/2)=(1-cos(x))/2	prove\:\sin^{2}(\frac{x}{2})=\frac{1-\cos(x)}{2}
prove cos(x+(3pi)/2)=sin(x)	prove\:\cos(x+\frac{3π}{2})=\sin(x)
prove 1-tan^4(A)=2sec^2(A)-sec^4(A)	prove\:1-\tan^{4}(A)=2\sec^{2}(A)-\sec^{4}(A)
prove cos^4(θ)-sin^4(θ)=2cos^2(θ)-1	prove\:\cos^{4}(θ)-\sin^{4}(θ)=2\cos^{2}(θ)-1
prove sin(x)tan(x)+cos(x)= 1/(cos(x))	prove\:\sin(x)\tan(x)+\cos(x)=\frac{1}{\cos(x)}
prove (1-cos(x))/(sin(x))=tan(x/2)	prove\:\frac{1-\cos(x)}{\sin(x)}=\tan(\frac{x}{2})
prove cos(4θ)=8cos^4(θ)-8cos^2(θ)+1	prove\:\cos(4θ)=8\cos^{4}(θ)-8\cos^{2}(θ)+1
prove 1-2cos^2(x)=2sin^2(x)-1	prove\:1-2\cos^{2}(x)=2\sin^{2}(x)-1
prove sin(2A)=2sin(A)cos(A)	prove\:\sin(2A)=2\sin(A)\cos(A)
prove tan(A-B)=sin(A-B)sec(A-B)	prove\:\tan(A-B)=\sin(A-B)\sec(A-B)
prove cot^2(θ)(1-cos^2(θ))=cos^2(θ)	prove\:\cot^{2}(θ)(1-\cos^{2}(θ))=\cos^{2}(θ)
prove sin(pi/3+x)-cos(pi/6+x)=sin(x)	prove\:\sin(\frac{π}{3}+x)-\cos(\frac{π}{6}+x)=\sin(x)
prove csc(2x)-cot(2x)=tan(x)	prove\:\csc(2x)-\cot(2x)=\tan(x)
prove sin^2(x)(cot^2(x)+1)=1	prove\:\sin^{2}(x)(\cot^{2}(x)+1)=1
prove tan^2(θ)=csc^2(θ)tan^2(θ)-1	prove\:\tan^{2}(θ)=\csc^{2}(θ)\tan^{2}(θ)-1
prove cos(x+pi/6)+sin(x-pi/3)=0	prove\:\cos(x+\frac{π}{6})+\sin(x-\frac{π}{3})=0
prove tanh^2(x)+sech^2(x)=1	prove\:\tanh^{2}(x)+\sech^{2}(x)=1
prove (cos(θ)sec(θ))/(cot(θ))=tan(θ)	prove\:\frac{\cos(θ)\sec(θ)}{\cot(θ)}=\tan(θ)
prove csc^2(u)-cos(u)sec(u)=cot^2(u)	prove\:\csc^{2}(u)-\cos(u)\sec(u)=\cot^{2}(u)
prove (cos^2(x))/(sin(x))+sin(x)=csc(x)	prove\:\frac{\cos^{2}(x)}{\sin(x)}+\sin(x)=\csc(x)
prove cos^2(x)tan^2(x)=1-cos^2(x)	prove\:\cos^{2}(x)\tan^{2}(x)=1-\cos^{2}(x)
prove-csc^2(x)cos^2(x)=1-csc^2(x)	prove\:-\csc^{2}(x)\cos^{2}(x)=1-\csc^{2}(x)
prove sec(θ)=sin(θ)(tan(θ)+cot(θ))	prove\:\sec(θ)=\sin(θ)(\tan(θ)+\cot(θ))
prove (csc^2(A))/(1+tan^2(A))=cot^2(A)	prove\:\frac{\csc^{2}(A)}{1+\tan^{2}(A)}=\cot^{2}(A)
prove sin(3a)=3sin(a)-4sin^3(a)	prove\:\sin(3a)=3\sin(a)-4\sin^{3}(a)
prove (sin(x)+tan(x))/(1+cos(x))=tan(x)	prove\:\frac{\sin(x)+\tan(x)}{1+\cos(x)}=\tan(x)
prove 1/(tan(θ)csc(θ))=cos(θ)	prove\:\frac{1}{\tan(θ)\csc(θ)}=\cos(θ)
prove tan(x)+sec(x)=(1+sin(x))/(cos(x))	prove\:\tan(x)+\sec(x)=\frac{1+\sin(x)}{\cos(x)}
prove 2cos^2(x/2)sec(x)=sec(x)+1	prove\:2\cos^{2}(\frac{x}{2})\sec(x)=\sec(x)+1
prove 1+cos^2(θ)=2cos^2(θ)+sin^2(θ)	prove\:1+\cos^{2}(θ)=2\cos^{2}(θ)+\sin^{2}(θ)
prove (1+sec(x))/(tan(x)+sin(x))=csc(x)	prove\:\frac{1+\sec(x)}{\tan(x)+\sin(x)}=\csc(x)
prove sec(θ)+tan(θ)= 1/(sec(θ)-tan(θ))	prove\:\sec(θ)+\tan(θ)=\frac{1}{\sec(θ)-\tan(θ)}
prove (1-sin(x))/(1-csc(x))=-sin(x)	prove\:\frac{1-\sin(x)}{1-\csc(x)}=-\sin(x)
prove 1+cos(10y)=2cos^2(5y)	prove\:1+\cos(10y)=2\cos^{2}(5y)
prove cos(a)tan(a)=sin(a)	prove\:\cos(a)\tan(a)=\sin(a)
prove sin(pi/6)= 1/2	prove\:\sin(\frac{π}{6})=\frac{1}{2}
prove cot(2x)= 1/2 cot(x)-1/2 tan(x)	prove\:\cot(2x)=\frac{1}{2}\cot(x)-\frac{1}{2}\tan(x)
prove (sin(t)-cos(t))^2=1-sin(2t)	prove\:(\sin(t)-\cos(t))^{2}=1-\sin(2t)
prove (1-sin(θ))(1+sin(θ))= 1/(sec^2(θ))	prove\:(1-\sin(θ))(1+\sin(θ))=\frac{1}{\sec^{2}(θ)}
prove sin(θ)=(2tan(θ/2))/(1+tan^2(θ/2))	prove\:\sin(θ)=\frac{2\tan(\frac{θ}{2})}{1+\tan^{2}(\frac{θ}{2})}
prove sin^2(x)-2cos^2(x)=1-3cos^2(x)	prove\:\sin^{2}(x)-2\cos^{2}(x)=1-3\cos^{2}(x)
prove 1/(sin^2(x))=csc^2(x)	prove\:\frac{1}{\sin^{2}(x)}=\csc^{2}(x)
prove (sin(x))/(1+cos(x))+cot(x)=csc(x)	prove\:\frac{\sin(x)}{1+\cos(x)}+\cot(x)=\csc(x)
prove cos(θ-pi/2)=sin(θ)	prove\:\cos(θ-\frac{π}{2})=\sin(θ)
prove csc(x)*cos(x)=cot(x)	prove\:\csc(x)\cdot\:\cos(x)=\cot(x)
prove cot(a)+tan(a)=2csc(2a)	prove\:\cot(a)+\tan(a)=2\csc(2a)
prove cot^2(x)=cos^2(x)+(cot(x)cos(x))^2	prove\:\cot^{2}(x)=\cos^{2}(x)+(\cot(x)\cos(x))^{2}
prove sin(-x)+cos(-x)=-sin(x)+cos(x)	prove\:\sin(-x)+\cos(-x)=-\sin(x)+\cos(x)
prove cot(θ)sec(θ)sin(θ)=1	prove\:\cot(θ)\sec(θ)\sin(θ)=1
prove (sec(θ))/(1-sin(θ))=(1+sin(θ))/(cos^3(θ))	prove\:\frac{\sec(θ)}{1-\sin(θ)}=\frac{1+\sin(θ)}{\cos^{3}(θ)}
prove tan(pi+θ)=tan(θ)	prove\:\tan(π+θ)=\tan(θ)
prove csc(θ)=cot(θ)sec(θ)	prove\:\csc(θ)=\cot(θ)\sec(θ)
prove (1-tan(x))/(sin(x))=csc(x)-sec(x)	prove\:\frac{1-\tan(x)}{\sin(x)}=\csc(x)-\sec(x)
prove sec(θ)sin(θ)cot(θ)=1	prove\:\sec(θ)\sin(θ)\cot(θ)=1
prove csc^2(x/2)= 2/(1-cos(x))	prove\:\csc^{2}(\frac{x}{2})=\frac{2}{1-\cos(x)}
prove (tan^2(θ))/(sin^2(θ))-1=tan^2(θ)	prove\:\frac{\tan^{2}(θ)}{\sin^{2}(θ)}-1=\tan^{2}(θ)
prove csc(θ)cos^2(θ)+sin(θ)=csc(θ)	prove\:\csc(θ)\cos^{2}(θ)+\sin(θ)=\csc(θ)
prove sec(θ+pi/2)=csc(θ)	prove\:\sec(θ+\frac{π}{2})=\csc(θ)
prove (1+csc(θ))/(sec(θ))-cot(θ)=cos(θ)	prove\:\frac{1+\csc(θ)}{\sec(θ)}-\cot(θ)=\cos(θ)
prove sin(2θ)=(2cot(θ))/(1+cot^2(θ))	prove\:\sin(2θ)=\frac{2\cot(θ)}{1+\cot^{2}(θ)}
prove cos(A)csc(A)=cot(A)	prove\:\cos(A)\csc(A)=\cot(A)
prove tan(θ)=(1-cos(2θ))/(sin(2θ))	prove\:\tan(θ)=\frac{1-\cos(2θ)}{\sin(2θ)}
prove cos^2(x)=sin^2(x)cos^2(x)+cos^4(x)	prove\:\cos^{2}(x)=\sin^{2}(x)\cos^{2}(x)+\cos^{4}(x)
prove (sin^2(x)cot(x))/(cos(x))=sin(x)	prove\:\frac{\sin^{2}(x)\cot(x)}{\cos(x)}=\sin(x)
prove csc(2θ)+cot(2θ)=cot(θ)	prove\:\csc(2θ)+\cot(2θ)=\cot(θ)
prove-tan(x)cos(x)=sin(-x)	prove\:-\tan(x)\cos(x)=\sin(-x)
prove sin(x-(3pi)/2)=cos(x)	prove\:\sin(x-\frac{3π}{2})=\cos(x)
prove cos(x+2pi)=cos(x)	prove\:\cos(x+2π)=\cos(x)
prove sin^2(x)=((1-cos(2x)))/2	prove\:\sin^{2}(x)=\frac{(1-\cos(2x))}{2}
prove (cot^2(x))/(1+csc(x))=csc(x)-1	prove\:\frac{\cot^{2}(x)}{1+\csc(x)}=\csc(x)-1
prove (sin^2(θ))/(1-cos(θ))=1+cos(θ)	prove\:\frac{\sin^{2}(θ)}{1-\cos(θ)}=1+\cos(θ)
prove csc(2θ)= 1/2 sec(θ)csc(θ)	prove\:\csc(2θ)=\frac{1}{2}\sec(θ)\csc(θ)
prove sin(x)(1+cot(x))=sin(x)+cos(x)	prove\:\sin(x)(1+\cot(x))=\sin(x)+\cos(x)
prove arcsin(x)= 1/(sin(x))	prove\:\arcsin(x)=\frac{1}{\sin(x)}
prove cot(pi/2-x)csc(x)=sec(x)	prove\:\cot(\frac{π}{2}-x)\csc(x)=\sec(x)
prove csc^2(x)+sec^2(x)=csc^2(x)sec^2(x)	prove\:\csc^{2}(x)+\sec^{2}(x)=\csc^{2}(x)\sec^{2}(x)
prove cos(60)=cos^2(30)-sin^2(30)	prove\:\cos(60^{\circ\:})=\cos^{2}(30^{\circ\:})-\sin^{2}(30^{\circ\:})
prove sec^2(θ)cot(θ)=tan(θ)+cot(θ)	prove\:\sec^{2}(θ)\cot(θ)=\tan(θ)+\cot(θ)
prove (1-cos^2(x))/(cos(x))=tan(x)sin(x)	prove\:\frac{1-\cos^{2}(x)}{\cos(x)}=\tan(x)\sin(x)
prove (sin^2(x))/(cos(x))+cos(x)=sec(x)	prove\:\frac{\sin^{2}(x)}{\cos(x)}+\cos(x)=\sec(x)
prove (cot(x)tan(x))/(sin(x))=csc(x)	prove\:\frac{\cot(x)\tan(x)}{\sin(x)}=\csc(x)
prove tan(6a)sec(3a)=2sin(3a)sec(6a)	prove\:\tan(6a)\sec(3a)=2\sin(3a)\sec(6a)

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