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Popular Trigonometry Problems

prove tan(θ)(cot(θ)+tan(θ))=sec^2(θ)	prove\:\tan(θ)(\cot(θ)+\tan(θ))=\sec^{2}(θ)
prove sec^2(-θ)-1=tan^2(θ)	prove\:\sec^{2}(-θ)-1=\tan^{2}(θ)
prove 2tan(x)=(cos(x))/(csc(x)-1)+(cos(x))/(csc(x)+1)	prove\:2\tan(x)=\frac{\cos(x)}{\csc(x)-1}+\frac{\cos(x)}{\csc(x)+1}
prove sin(-θ)sec(-θ)cot(-θ)=1	prove\:\sin(-θ)\sec(-θ)\cot(-θ)=1
prove cos^4(θ)-sin^4(θ)=1-2sin^2(θ)	prove\:\cos^{4}(θ)-\sin^{4}(θ)=1-2\sin^{2}(θ)
prove cot(x)sin(x)sec^2(x)=sec(x)	prove\:\cot(x)\sin(x)\sec^{2}(x)=\sec(x)
prove tan(2x)=(sin(2x))/(cos(2x))	prove\:\tan(2x)=\frac{\sin(2x)}{\cos(2x)}
prove sin^2(x)+4cos^2(x)=4-3sin^2(x)	prove\:\sin^{2}(x)+4\cos^{2}(x)=4-3\sin^{2}(x)
prove sin(a+b)=sin(a)cos(b)+cos(a)sin(b)	prove\:\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)
prove 1/(1-cos(x))=(1+cos(x))/(sin^2(x))	prove\:\frac{1}{1-\cos(x)}=\frac{1+\cos(x)}{\sin^{2}(x)}
prove tan(θ+pi/2)=-cot(θ)	prove\:\tan(θ+\frac{π}{2})=-\cot(θ)
prove sin(B)+cos(B)cot(B)=csc(B)	prove\:\sin(B)+\cos(B)\cot(B)=\csc(B)
prove 3sin(5pi-x)=3sin(x)	prove\:3\sin(5π-x)=3\sin(x)
prove cos^2(θ)=(1+cos(2θ))/2	prove\:\cos^{2}(θ)=\frac{1+\cos(2θ)}{2}
prove 1-((sin^2(x)))/(1-cos(x))=-cos(x)	prove\:1-\frac{(\sin^{2}(x))}{1-\cos(x)}=-\cos(x)
prove (cos^2(α))/(1-sin(α))=1+sin(α)	prove\:\frac{\cos^{2}(α)}{1-\sin(α)}=1+\sin(α)
prove 2sin^2(θ)-1=1-2cos^2(θ)	prove\:2\sin^{2}(θ)-1=1-2\cos^{2}(θ)
prove cos(θ-pi)=-cos(θ)	prove\:\cos(θ-π)=-\cos(θ)
prove (tan^2(x))/(sin^2(x))=tan^2(x)+1	prove\:\frac{\tan^{2}(x)}{\sin^{2}(x)}=\tan^{2}(x)+1
prove csc(A-B)=(csc(A)csc(B))/(cot(B)-cot(A))	prove\:\csc(A-B)=\frac{\csc(A)\csc(B)}{\cot(B)-\cot(A)}
prove (cot^2(θ))/(csc^2(θ))=cos^2(θ)	prove\:\frac{\cot^{2}(θ)}{\csc^{2}(θ)}=\cos^{2}(θ)
prove (csc(a)+1)(csc(a)-1)=cot^2(a)	prove\:(\csc(a)+1)(\csc(a)-1)=\cot^{2}(a)
prove (sec(x))(csc(x))=cot(x)+tan(x)	prove\:(\sec(x))(\csc(x))=\cot(x)+\tan(x)
prove (cos(θ))/(1+sin(θ))=sec(θ)-tan(θ)	prove\:\frac{\cos(θ)}{1+\sin(θ)}=\sec(θ)-\tan(θ)
prove 2cos^2(A)-1=1-2sin^2(A)	prove\:2\cos^{2}(A)-1=1-2\sin^{2}(A)
prove sec^4(t)-tan^4(t)=1+2tan^2(t)	prove\:\sec^{4}(t)-\tan^{4}(t)=1+2\tan^{2}(t)
prove cos(4θ)=cos^2(2θ)-sin^2(2θ)	prove\:\cos(4θ)=\cos^{2}(2θ)-\sin^{2}(2θ)
prove sec(x)csc(x)-cot(x)=tan(x)	prove\:\sec(x)\csc(x)-\cot(x)=\tan(x)
prove tan(θ)sin(2θ)=2-2cos^2(θ)	prove\:\tan(θ)\sin(2θ)=2-2\cos^{2}(θ)
prove-30cos(3x)sin(3x)=-15sin(6x)	prove\:-30\cos(3x)\sin(3x)=-15\sin(6x)
prove 2sin^2(θ)-1=sin^4(θ)-cos^4(θ)	prove\:2\sin^{2}(θ)-1=\sin^{4}(θ)-\cos^{4}(θ)
prove csc(2θ)=(1+cot^2(θ))/(2cot(θ))	prove\:\csc(2θ)=\frac{1+\cot^{2}(θ)}{2\cot(θ)}
prove csc^4(θ)-cot^4(θ)=2cot^2(θ)+1	prove\:\csc^{4}(θ)-\cot^{4}(θ)=2\cot^{2}(θ)+1
prove sec(b)cot(b)=csc(b)	prove\:\sec(b)\cot(b)=\csc(b)
prove (1-cos(2θ))/(sin(2θ))=tan(θ)	prove\:\frac{1-\cos(2θ)}{\sin(2θ)}=\tan(θ)
prove (cos(3x))/(sin(x))+(sin(3x))/(cos(x))=2cot(2x)	prove\:\frac{\cos(3x)}{\sin(x)}+\frac{\sin(3x)}{\cos(x)}=2\cot(2x)
prove sin(A+B)=sin(A)+sin(B)	prove\:\sin(A+B)=\sin(A)+\sin(B)
prove (cot^2(B)-cos^2(B))/(csc^2(B)-1)=cos^2(B)	prove\:\frac{\cot^{2}(B)-\cos^{2}(B)}{\csc^{2}(B)-1}=\cos^{2}(B)
prove cos(2a)=1-2sin^2(a)	prove\:\cos(2a)=1-2\sin^{2}(a)
prove sec^2(x)-tan^2(x)=tan(x)cot(x)	prove\:\sec^{2}(x)-\tan^{2}(x)=\tan(x)\cot(x)
prove (tan(θ))/(tan(θ)-1)= 1/(1-cot(θ))	prove\:\frac{\tan(θ)}{\tan(θ)-1}=\frac{1}{1-\cot(θ)}
prove csc(u)-sin(u)=cos(u)cot(u)	prove\:\csc(u)-\sin(u)=\cos(u)\cot(u)
prove (tan^2(x))/(sec(x)-1)=sec(x)+1	prove\:\frac{\tan^{2}(x)}{\sec(x)-1}=\sec(x)+1
prove (1+tan^2(x))/(csc(x)sec(x))=tan(x)	prove\:\frac{1+\tan^{2}(x)}{\csc(x)\sec(x)}=\tan(x)
prove (sin(θ))/(csc(θ)-cot(θ))=1+cos(θ)	prove\:\frac{\sin(θ)}{\csc(θ)-\cot(θ)}=1+\cos(θ)
prove sec(θ)-tan(θ)sin(θ)= 1/(sec(θ))	prove\:\sec(θ)-\tan(θ)\sin(θ)=\frac{1}{\sec(θ)}
prove cot(-a)cos(-a)+sin(-a)=-csc(a)	prove\:\cot(-a)\cos(-a)+\sin(-a)=-\csc(a)
prove sin(2a)-tan(a)=tan(a)cos(2a)	prove\:\sin(2a)-\tan(a)=\tan(a)\cos(2a)
prove 2cos(x)tan(x)csc(x)=2	prove\:2\cos(x)\tan(x)\csc(x)=2
prove sec^2(y)-cot^2(pi/2-y)=1	prove\:\sec^{2}(y)-\cot^{2}(\frac{π}{2}-y)=1
prove sin(pi/3+x)-sin(pi/3-x)=sin(x)	prove\:\sin(\frac{π}{3}+x)-\sin(\frac{π}{3}-x)=\sin(x)
prove 1+cos(2x)=2cos^2(x)	prove\:1+\cos(2x)=2\cos^{2}(x)
prove tan(x)(csc(x)-sin(x))=cos(x)	prove\:\tan(x)(\csc(x)-\sin(x))=\cos(x)
prove tan(x)(sin(x)+cot(x)cos(x))=sec(x)	prove\:\tan(x)(\sin(x)+\cot(x)\cos(x))=\sec(x)
prove sin(x)cos^2(x)+sin^3(x)=sin(x)	prove\:\sin(x)\cos^{2}(x)+\sin^{3}(x)=\sin(x)
prove (csc(x)+sec(x))/(tan(x)+1)=csc(x)	prove\:\frac{\csc(x)+\sec(x)}{\tan(x)+1}=\csc(x)
prove cos(pi/3)= 1/2	prove\:\cos(\frac{π}{3})=\frac{1}{2}
prove sec(-x)=sec(x)	prove\:\sec(-x)=\sec(x)
prove cos(pi/3+x)+cos(pi/3-x)=cos(x)	prove\:\cos(\frac{π}{3}+x)+\cos(\frac{π}{3}-x)=\cos(x)
prove (csc(θ))/(cot(θ)+tan(θ))=cos(θ)	prove\:\frac{\csc(θ)}{\cot(θ)+\tan(θ)}=\cos(θ)
prove sec^2(x)+tan^2(x)=2sec^2(x)-1	prove\:\sec^{2}(x)+\tan^{2}(x)=2\sec^{2}(x)-1
prove cos^2(2x)=(1+cos(4x))/2	prove\:\cos^{2}(2x)=\frac{1+\cos(4x)}{2}
prove sin^2(θ)csc^2(θ)-sin^2(θ)=cos^2(θ)	prove\:\sin^{2}(θ)\csc^{2}(θ)-\sin^{2}(θ)=\cos^{2}(θ)
prove cos(x+pi/3)+sin(x-pi/6)=0	prove\:\cos(x+\frac{π}{3})+\sin(x-\frac{π}{6})=0
prove (1-tan^2(b))/(1+tan^2(b))=cos(2b)	prove\:\frac{1-\tan^{2}(b)}{1+\tan^{2}(b)}=\cos(2b)
prove (sin(θ)+cos(θ))/(cos(θ))=1+tan(θ)	prove\:\frac{\sin(θ)+\cos(θ)}{\cos(θ)}=1+\tan(θ)
prove 8/(cos(x)+1)+8/(cos(x)-1)=-16csc(x)cot(x)	prove\:\frac{8}{\cos(x)+1}+\frac{8}{\cos(x)-1}=-16\csc(x)\cot(x)
prove sec(x)(sec(x)-cos(x))=tan^2(x)	prove\:\sec(x)(\sec(x)-\cos(x))=\tan^{2}(x)
prove 1/(sin(x))-sin(x)=cot(x)cos(x)	prove\:\frac{1}{\sin(x)}-\sin(x)=\cot(x)\cos(x)
prove sin(3x)=3sin(x)-4(sin(x))^3	prove\:\sin(3x)=3\sin(x)-4(\sin(x))^{3}
prove (5sin(θ)-5cos(θ))^2=25-25sin(2θ)	prove\:(5\sin(θ)-5\cos(θ))^{2}=25-25\sin(2θ)
prove (sin(θ)-1)/(cos(θ))=tan(θ)-sec(θ)	prove\:\frac{\sin(θ)-1}{\cos(θ)}=\tan(θ)-\sec(θ)
prove cot(x)*sec(x)=csc(x)	prove\:\cot(x)\cdot\:\sec(x)=\csc(x)
prove 2-csc^2(θ)=1-cot^2(θ)	prove\:2-\csc^{2}(θ)=1-\cot^{2}(θ)
prove 1-(cos^2(x))/(1-sin(x))=-sin(x)	prove\:1-\frac{\cos^{2}(x)}{1-\sin(x)}=-\sin(x)
prove sin(x)= 1/(csc(x))	prove\:\sin(x)=\frac{1}{\csc(x)}
prove-tan(t)+(cos(t))/(1-sin(t))=sec(t)	prove\:-\tan(t)+\frac{\cos(t)}{1-\sin(t)}=\sec(t)
prove cot^4(x)-csc^4(x)=1-2csc^2(x)	prove\:\cot^{4}(x)-\csc^{4}(x)=1-2\csc^{2}(x)
prove cos(x)=sin(pi/2-x)	prove\:\cos(x)=\sin(\frac{π}{2}-x)
prove cos(x)=sin(x)cot(x)	prove\:\cos(x)=\sin(x)\cot(x)
prove cos^2(θ/2)=(sec(θ)+1)/(2sec(θ))	prove\:\cos^{2}(\frac{θ}{2})=\frac{\sec(θ)+1}{2\sec(θ)}
prove cos^2(x)=(cos(x))^2	prove\:\cos^{2}(x)=(\cos(x))^{2}
prove 2cos^2(θ)tan(θ)=sin(2θ)	prove\:2\cos^{2}(θ)\tan(θ)=\sin(2θ)
prove sin^5(x)=(1-cos^2(x))^2sin(x)	prove\:\sin^{5}(x)=(1-\cos^{2}(x))^{2}\sin(x)
prove csc(x)sec(x)=cot(x)+tan(x)	prove\:\csc(x)\sec(x)=\cot(x)+\tan(x)
prove cos((3pi)/2-x)=-sin(x)	prove\:\cos(\frac{3π}{2}-x)=-\sin(x)
prove (cos(a))/(tan(a))=csc(a)-sin(a)	prove\:\frac{\cos(a)}{\tan(a)}=\csc(a)-\sin(a)
prove sin(x)tan(x/2)=1-cos(x)	prove\:\sin(x)\tan(\frac{x}{2})=1-\cos(x)
prove cot(t)+(sin(t))/(1+cos(t))=csc(t)	prove\:\cot(t)+\frac{\sin(t)}{1+\cos(t)}=\csc(t)
prove sin(pi+θ)=-sin(θ)	prove\:\sin(π+θ)=-\sin(θ)
prove (tan(x)cot(x))/(sin(x))=csc(x)	prove\:\frac{\tan(x)\cot(x)}{\sin(x)}=\csc(x)
prove csc^2(θ/2)=(2sec(θ))/(sec(θ)-1)	prove\:\csc^{2}(\frac{θ}{2})=\frac{2\sec(θ)}{\sec(θ)-1}
prove csc^2(x)*tan^2(x)-1=tan^2(x)	prove\:\csc^{2}(x)\cdot\:\tan^{2}(x)-1=\tan^{2}(x)
prove (1+csc(θ))/(sec(θ))=cos(θ)+cot(θ)	prove\:\frac{1+\csc(θ)}{\sec(θ)}=\cos(θ)+\cot(θ)
prove (cos(x))/(sec(2x))-(sin(x))/(csc(2x))=cos(3x)	prove\:\frac{\cos(x)}{\sec(2x)}-\frac{\sin(x)}{\csc(2x)}=\cos(3x)
prove cot(a)+(sin(a))/(1+cos(a))=csc(a)	prove\:\cot(a)+\frac{\sin(a)}{1+\cos(a)}=\csc(a)
prove sec^2(x)-cot^2(pi/2-x)=1	prove\:\sec^{2}(x)-\cot^{2}(\frac{π}{2}-x)=1
prove cos^2(x)=((1+cos(2x)))/2	prove\:\cos^{2}(x)=\frac{(1+\cos(2x))}{2}
prove sin(2x)=-2sin(-x)cos(-x)	prove\:\sin(2x)=-2\sin(-x)\cos(-x)
prove sin(θ)csc(θ)-sin^2(θ)=cos^2(θ)	prove\:\sin(θ)\csc(θ)-\sin^{2}(θ)=\cos^{2}(θ)

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