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Popular Trigonometry Problems

prove (sec(v)-cos(v))/(sec(v))=sin^2(v)	prove\:\frac{\sec(v)-\cos(v)}{\sec(v)}=\sin^{2}(v)
prove csc^2(θ)(1-cos^2(θ))=tan(420)	prove\:\csc^{2}(θ)(1-\cos^{2}(θ))=\tan(420^{\circ\:})
prove 1/((1-\frac{1){(1-1/((1-cosh^2(x))))})}=cosh^2(x)	prove\:\frac{1}{(1-\frac{1}{(1-\frac{1}{(1-\cosh^{2}(x))})})}=\cosh^{2}(x)
prove ((sec(θ))/(cos(θ)))-((tan(θ))/(cot(θ)))=1	prove\:(\frac{\sec(θ)}{\cos(θ)})-(\frac{\tan(θ)}{\cot(θ)})=1
prove sin(pi)=sin(3pi)	prove\:\sin(π)=\sin(3π)
prove (2+csc(x))/(sec(x))-2cos(x)=cot(x)	prove\:\frac{2+\csc(x)}{\sec(x)}-2\cos(x)=\cot(x)
prove (cos(60))/(sin(60))=cot(60)	prove\:\frac{\cos(60^{\circ\:})}{\sin(60^{\circ\:})}=\cot(60^{\circ\:})
prove 1/(sec(x)(sec(x)-cos(x)))=cot^2(x)	prove\:\frac{1}{\sec(x)(\sec(x)-\cos(x))}=\cot^{2}(x)
prove sec(30)-sin(30)tan(30)=cos(30)	prove\:\sec(30^{\circ\:})-\sin(30^{\circ\:})\tan(30^{\circ\:})=\cos(30^{\circ\:})
prove tan(x)*csc^2(x)-tan(x)=cot(x)	prove\:\tan(x)\cdot\:\csc^{2}(x)-\tan(x)=\cot(x)
prove 2sin^2(2x)+cos(4x)=1	prove\:2\sin^{2}(2x)+\cos(4x)=1
prove cos(α-β)-cos(α+β)=2sin(α)sin(β)	prove\:\cos(α-β)-\cos(α+β)=2\sin(α)\sin(β)
prove 1=sec^2(θ)-tan^2(θ)	prove\:1=\sec^{2}(θ)-\tan^{2}(θ)
prove tan^8(x)=tan^6(x)sec^2(x)-tan^6(x)	prove\:\tan^{8}(x)=\tan^{6}(x)\sec^{2}(x)-\tan^{6}(x)
prove 2(sin(2y)cos(2y))=sin(4y)	prove\:2(\sin(2y)\cos(2y))=\sin(4y)
prove ((tan^2(t)))/(sec(t))=sec(t)-cos(t)	prove\:\frac{(\tan^{2}(t))}{\sec(t)}=\sec(t)-\cos(t)
prove-sin(-1)=sin(1)	prove\:-\sin(-1)=\sin(1)
prove sin^2(y)cos^2(y)=(1-cos(4x))/8	prove\:\sin^{2}(y)\cos^{2}(y)=\frac{1-\cos(4x)}{8}
prove (sin(2x))/(1-cos(2x))=(cos(x))/(sin(x))	prove\:\frac{\sin(2x)}{1-\cos(2x)}=\frac{\cos(x)}{\sin(x)}
prove ((cos(a-b)))/(sin(a)sin(b))=cot(a)cot(b)+1	prove\:\frac{(\cos(a-b))}{\sin(a)\sin(b)}=\cot(a)\cot(b)+1
prove 2cos(x)(sin(3x)-sin(x))=sin(4x)	prove\:2\cos(x)(\sin(3x)-\sin(x))=\sin(4x)
prove (1-sin(θ))/(sec(θ))=(cos^3(θ))/(1+sin(θ))	prove\:\frac{1-\sin(θ)}{\sec(θ)}=\frac{\cos^{3}(θ)}{1+\sin(θ)}
prove 5sin^2(x)+5cos^2(x)=5	prove\:5\sin^{2}(x)+5\cos^{2}(x)=5
prove cot(θ)=((1+cos(2θ)))/(sin(2θ))	prove\:\cot(θ)=\frac{(1+\cos(2θ))}{\sin(2θ)}
prove 1+(tan^2(A))/(1+sec(A))=sec(A)	prove\:1+\frac{\tan^{2}(A)}{1+\sec(A)}=\sec(A)
prove tan^2(23)-sec^2(23)=-1	prove\:\tan^{2}(23^{\circ\:})-\sec^{2}(23^{\circ\:})=-1
prove (1-cos^2(t))(1+cos^2(t))=1	prove\:(1-\cos^{2}(t))(1+\cos^{2}(t))=1
prove tan(135+a)=(tan(a)-1)/(tan(a)+1)	prove\:\tan(135^{\circ\:}+a)=\frac{\tan(a)-1}{\tan(a)+1}
prove (1-cos^2(A))(1+cot^2(A))=1	prove\:(1-\cos^{2}(A))(1+\cot^{2}(A))=1
prove 4cos^2(x)+cos(2x)=5-6sin^2(x)	prove\:4\cos^{2}(x)+\cos(2x)=5-6\sin^{2}(x)
prove (sin^2(2x))/4 =sin^2(x)cos^2(x)	prove\:\frac{\sin^{2}(2x)}{4}=\sin^{2}(x)\cos^{2}(x)
prove (sec(θ))/(tan(θ)+cot(θ))=sin(θ)	prove\:\frac{\sec(θ)}{\tan(θ)+\cot(θ)}=\sin(θ)
prove (sin(2x))/(cos(2x)+sin^2(x))=2tan(x)	prove\:\frac{\sin(2x)}{\cos(2x)+\sin^{2}(x)}=2\tan(x)
prove 7cos^2(x)+5sin^2(x)=6+cos(2x)	prove\:7\cos^{2}(x)+5\sin^{2}(x)=6+\cos(2x)
prove 2/(1-cos(2x))=csc^2(x)	prove\:\frac{2}{1-\cos(2x)}=\csc^{2}(x)
prove cos(10x)-cos(6x)=-2sin(8x)sin(2x)	prove\:\cos(10x)-\cos(6x)=-2\sin(8x)\sin(2x)
prove (1+cos(2x))/(cos(x))=2cos(x)	prove\:\frac{1+\cos(2x)}{\cos(x)}=2\cos(x)
prove sec(y)-cos(y)=tan(y)sin(y)	prove\:\sec(y)-\cos(y)=\tan(y)\sin(y)
prove sin(5x)-sin(3x)=2cos(4x)sin(x)	prove\:\sin(5x)-\sin(3x)=2\cos(4x)\sin(x)
prove sin(40)=2sin(20)cos(20)	prove\:\sin(40^{\circ\:})=2\sin(20^{\circ\:})\cos(20^{\circ\:})
prove sin(θ)-cos^2(θ)sin(θ)=sin^3(θ)	prove\:\sin(θ)-\cos^{2}(θ)\sin(θ)=\sin^{3}(θ)
prove sec^2(x)+csc^2(x)=(sec(x)csc(x))^2	prove\:\sec^{2}(x)+\csc^{2}(x)=(\sec(x)\csc(x))^{2}
prove (1+sin(x))/(sin(x))=1+csc(x)	prove\:\frac{1+\sin(x)}{\sin(x)}=1+\csc(x)
prove cos(2y)=(1-tan^2(y))/(1+tan^2(y))	prove\:\cos(2y)=\frac{1-\tan^{2}(y)}{1+\tan^{2}(y)}
prove 5sec^2(x)+4=9sec^2(x)-4tan^2(x)	prove\:5\sec^{2}(x)+4=9\sec^{2}(x)-4\tan^{2}(x)
prove cos(20pi-x)+sin((83pi)/2+x)=0	prove\:\cos(20π-x)+\sin(\frac{83π}{2}+x)=0
prove sin(x)sin(2x)+cos(x)cos(2x)=cos(x)	prove\:\sin(x)\sin(2x)+\cos(x)\cos(2x)=\cos(x)
prove 45-25sin(-120pit)=45+25sin(120pit)	prove\:45-25\sin(-120πt)=45+25\sin(120πt)
prove cos^2(x)-sin^2(y)=1-2sin^2(y)	prove\:\cos^{2}(x)-\sin^{2}(y)=1-2\sin^{2}(y)
prove sin(3x)+sin(x)=2sin(2x)cos(x)	prove\:\sin(3x)+\sin(x)=2\sin(2x)\cos(x)
prove (2cot(x))/(1+cot^2(x))=sin(2x)	prove\:\frac{2\cot(x)}{1+\cot^{2}(x)}=\sin(2x)
prove sec(-x)=-sec(x)	prove\:\sec(-x)=-\sec(x)
prove ((sin^2(x)))/(1-cos(x))=1+cos(x)	prove\:\frac{(\sin^{2}(x))}{1-\cos(x)}=1+\cos(x)
prove (tan(x))/(csc(x))= 1/(cos(x))-1/(sec(x))	prove\:\frac{\tan(x)}{\csc(x)}=\frac{1}{\cos(x)}-\frac{1}{\sec(x)}
prove cos^2(b)+sin^2(b)=1	prove\:\cos^{2}(b)+\sin^{2}(b)=1
prove (cos(θ)+cos(3θ))/(2cos(θ))=cos(2θ)	prove\:\frac{\cos(θ)+\cos(3θ)}{2\cos(θ)}=\cos(2θ)
prove 3tan(x)=4sin(x)	prove\:3\tan(x)=4\sin(x)
prove sin(x)+cos(x)=sqrt(2)sin(x+pi/4)	prove\:\sin(x)+\cos(x)=\sqrt{2}\sin(x+\frac{π}{4})
prove (sin(t))cot(t)=cos(t)	prove\:(\sin(t))\cot(t)=\cos(t)
prove cos(θ)=sqrt(1-sin^2(θ))	prove\:\cos(θ)=\sqrt{1-\sin^{2}(θ)}
prove (cot^3(t))/(csc(t))=cos(t)cot^2(t)	prove\:\frac{\cot^{3}(t)}{\csc(t)}=\cos(t)\cot^{2}(t)
prove tan(pi/2-θ)sin(θ)=cos(θ)	prove\:\tan(\frac{π}{2}-θ)\sin(θ)=\cos(θ)
prove sin((5pi)/3)=-(sqrt(3))/2	prove\:\sin(\frac{5π}{3})=-\frac{\sqrt{3}}{2}
prove (sin(x))/(1-sin(x))+(sin(x))/(1+sin(x))=(2tan(x))/(cos(x))	prove\:\frac{\sin(x)}{1-\sin(x)}+\frac{\sin(x)}{1+\sin(x)}=\frac{2\tan(x)}{\cos(x)}
prove (2cos(x))/(cos^2(x))=2sec(x)	prove\:\frac{2\cos(x)}{\cos^{2}(x)}=2\sec(x)
prove cos(x+pi)+sin(x-(3pi)/2)=0	prove\:\cos(x+π)+\sin(x-\frac{3π}{2})=0
prove cos^4(A)-sin^4(A)+1=2cos^2(A)	prove\:\cos^{4}(A)-\sin^{4}(A)+1=2\cos^{2}(A)
prove 1-tan^4(θ)=2sec^2(θ)-sec^4(θ)	prove\:1-\tan^{4}(θ)=2\sec^{2}(θ)-\sec^{4}(θ)
prove 7sec(y)cos(y)=7	prove\:7\sec(y)\cos(y)=7
prove sec(pi/2-u)=csc(u)	prove\:\sec(\frac{π}{2}-u)=\csc(u)
prove (cot^3(t))/(csc(t))=cos(t)(csc^2(-1))	prove\:\frac{\cot^{3}(t)}{\csc(t)}=\cos(t)(\csc^{2}(-1))
prove (sec^2(x)cot(x))/(csc^2(x))=tan(x)	prove\:\frac{\sec^{2}(x)\cot(x)}{\csc^{2}(x)}=\tan(x)
prove (sec^2(y))/(tan(y))=tan(y)+cot(y)	prove\:\frac{\sec^{2}(y)}{\tan(y)}=\tan(y)+\cot(y)
prove cos(6x)=1-2sin^2(3x)	prove\:\cos(6x)=1-2\sin^{2}(3x)
prove tan(x-360)=tan(x)	prove\:\tan(x-360^{\circ\:})=\tan(x)
prove cos^2(x)-1=-sin^2(x)	prove\:\cos^{2}(x)-1=-\sin^{2}(x)
prove ((1-cos(-x)))/(sec(-x)-1)=cos(x)	prove\:\frac{(1-\cos(-x))}{\sec(-x)-1}=\cos(x)
prove 1-cot^2(θ)=2-csc^2(θ)	prove\:1-\cot^{2}(θ)=2-\csc^{2}(θ)
prove cos(-θ+pi/2)=sin(θ)	prove\:\cos(-θ+\frac{π}{2})=\sin(θ)
prove 1-sin(2x)csc(x)=cos(x)cot(x)	prove\:1-\sin(2x)\csc(x)=\cos(x)\cot(x)
prove (cos(2x))/(1-sin^2(x))=2-sec^2(x)	prove\:\frac{\cos(2x)}{1-\sin^{2}(x)}=2-\sec^{2}(x)
prove cot(-θ)*cos(-θ)+sin(-θ)=-csc(θ)	prove\:\cot(-θ)\cdot\:\cos(-θ)+\sin(-θ)=-\csc(θ)
prove sec(θ)cot(θ)-sin(θ)=cos(θ)cot(θ)	prove\:\sec(θ)\cot(θ)-\sin(θ)=\cos(θ)\cot(θ)
prove 9sin(9pi-x)=9sin(x)	prove\:9\sin(9π-x)=9\sin(x)
prove tan^4(θ)-sec^4(θ)=1-2sec^2(θ)	prove\:\tan^{4}(θ)-\sec^{4}(θ)=1-2\sec^{2}(θ)
prove sec(x)-tan(x)=cos(x)	prove\:\sec(x)-\tan(x)=\cos(x)
prove tan(2x)-tan(x)=(tan(x))/(cos(2x))	prove\:\tan(2x)-\tan(x)=\frac{\tan(x)}{\cos(2x)}
prove (cos^2(t))/(cot(t))=cos(t)sin(t)	prove\:\frac{\cos^{2}(t)}{\cot(t)}=\cos(t)\sin(t)
prove 4sec^2(θ)-3=1+4tan^2(θ)	prove\:4\sec^{2}(θ)-3=1+4\tan^{2}(θ)
prove-sin(x)=sin(x)	prove\:-\sin(x)=\sin(x)
prove sec(x)+tan(x)=(1/(sec(x)-tan(x)))	prove\:\sec(x)+\tan(x)=(\frac{1}{\sec(x)-\tan(x)})
prove sec(x-pi/2)=csc(x)	prove\:\sec(x-\frac{π}{2})=\csc(x)
prove cos(2v)=(1-tan^2(v))/(1+tan^2(v))	prove\:\cos(2v)=\frac{1-\tan^{2}(v)}{1+\tan^{2}(v)}
prove sin(A)= 1/(csc(A))	prove\:\sin(A)=\frac{1}{\csc(A)}
prove 9/(tan(x))+9/(cot(x))=9tan(x)+9cot(x)	prove\:\frac{9}{\tan(x)}+\frac{9}{\cot(x)}=9\tan(x)+9\cot(x)
prove sin(2x)cos(2x)=4sin(x)cos(x)	prove\:\sin(2x)\cos(2x)=4\sin(x)\cos(x)
prove sin(pi/6+x)=cos(pi/3-x)	prove\:\sin(\frac{π}{6}+x)=\cos(\frac{π}{3}-x)
prove (1+cos(2θ))(1-cos(2θ))=sin^2(2θ)	prove\:(1+\cos(2θ))(1-\cos(2θ))=\sin^{2}(2θ)
prove sin(2θ)+cos(2θ)=2sin(θ)cos(θ)+2cos^2(θ)-1	prove\:\sin(2θ)+\cos(2θ)=2\sin(θ)\cos(θ)+2\cos^{2}(θ)-1
prove cos(270-θ)=-sin(θ)	prove\:\cos(270^{\circ\:}-θ)=-\sin(θ)

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