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Popular Trigonometry Problems

prove (csc^2(x)-1)(sec^2(x)-1)=1	prove\:(\csc^{2}(x)-1)(\sec^{2}(x)-1)=1
prove cos(x)+sin(x)*tan(x)=sec(x)	prove\:\cos(x)+\sin(x)\cdot\:\tan(x)=\sec(x)
prove cot(x)+1=csc(x)(cos(x)+sin(x))	prove\:\cot(x)+1=\csc(x)(\cos(x)+\sin(x))
prove (csc(x)-cot(x))/(csc(x))=1-cos(x)	prove\:\frac{\csc(x)-\cot(x)}{\csc(x)}=1-\cos(x)
prove (sin^2(x))/(cos(x)-1)=-1-cos(x)	prove\:\frac{\sin^{2}(x)}{\cos(x)-1}=-1-\cos(x)
prove (7cot(x))/(sec(x))=7csc(x)-7sin(x)	prove\:\frac{7\cot(x)}{\sec(x)}=7\csc(x)-7\sin(x)
prove sin(θ+pi/3)=sin(θ)+sin(pi/3)	prove\:\sin(θ+\frac{π}{3})=\sin(θ)+\sin(\frac{π}{3})
prove (4sin(θ)-4cos(θ))^2=16-16sin(2θ)	prove\:(4\sin(θ)-4\cos(θ))^{2}=16-16\sin(2θ)
prove arcsec(x)=cos(x)	prove\:\arcsec(x)=\cos(x)
prove (csc(θ)-cot(θ))(1+sec(θ))=tan(θ)	prove\:(\csc(θ)-\cot(θ))(1+\sec(θ))=\tan(θ)
prove (1-sin^2(b))/(cos(b))=cos(b)	prove\:\frac{1-\sin^{2}(b)}{\cos(b)}=\cos(b)
prove (1+csc(θ))/(cot(θ)+cos(θ))=sec(θ)	prove\:\frac{1+\csc(θ)}{\cot(θ)+\cos(θ)}=\sec(θ)
prove cos(3θ)=cos(θ)	prove\:\cos(3θ)=\cos(θ)
prove 1/(1-sin(x))=(1+sin(x))/(cos^2(x))	prove\:\frac{1}{1-\sin(x)}=\frac{1+\sin(x)}{\cos^{2}(x)}
prove tan^2(x)*cos^2(x)=1-cos^2(x)	prove\:\tan^{2}(x)\cdot\:\cos^{2}(x)=1-\cos^{2}(x)
prove sin^2(A)-sin^2(A)cos^2(A)=sin^4(A)	prove\:\sin^{2}(A)-\sin^{2}(A)\cos^{2}(A)=\sin^{4}(A)
prove 1/(sin(x)cos(x))=sec(x)csc(x)	prove\:\frac{1}{\sin(x)\cos(x)}=\sec(x)\csc(x)
prove cot^2(x)+csc^2(x)=1+2cot^2(x)	prove\:\cot^{2}(x)+\csc^{2}(x)=1+2\cot^{2}(x)
prove sin(a)sec(a)tan(a)+1=sec^2(a)	prove\:\sin(a)\sec(a)\tan(a)+1=\sec^{2}(a)
prove (tan(y)+cot(y))/(csc(y))=sec(y)	prove\:\frac{\tan(y)+\cot(y)}{\csc(y)}=\sec(y)
prove (sec^2(a)-1)/(sec^2(a))=sin^2(a)	prove\:\frac{\sec^{2}(a)-1}{\sec^{2}(a)}=\sin^{2}(a)
prove 1/(sec(x))=sec(x)-tan(x)*sin(x)	prove\:\frac{1}{\sec(x)}=\sec(x)-\tan(x)\cdot\:\sin(x)
prove 2sin^2(x)-sin(x)-1=0	prove\:2\sin^{2}(x)-\sin(x)-1=0
prove 2cos^2(θ)-1=cos(2θ)	prove\:2\cos^{2}(θ)-1=\cos(2θ)
prove cos(3B)=cos(B)(cos^2(B)-3sin^2(B))	prove\:\cos(3B)=\cos(B)(\cos^{2}(B)-3\sin^{2}(B))
prove tan(2x)= 1/(1-tan(x))-1/(1+tan(x))	prove\:\tan(2x)=\frac{1}{1-\tan(x)}-\frac{1}{1+\tan(x)}
prove sin(θ+pi/2)=cos(θ)	prove\:\sin(θ+\frac{π}{2})=\cos(θ)
prove sin(2x)=(2cot(x))/(csc^2(x))	prove\:\sin(2x)=\frac{2\cot(x)}{\csc^{2}(x)}
prove (1-cos(x))(1+sec(x))=sec(x)-cos(x)	prove\:(1-\cos(x))(1+\sec(x))=\sec(x)-\cos(x)
prove 6sin(5pi-x)=6sin(x)	prove\:6\sin(5π-x)=6\sin(x)
prove (3cot(x))/(sec(x))=3csc(x)-3sin(x)	prove\:\frac{3\cot(x)}{\sec(x)}=3\csc(x)-3\sin(x)
prove 2sin(θ)cos(θ)=sin(2θ)	prove\:2\sin(θ)\cos(θ)=\sin(2θ)
prove tan^4(x)+tan^2(x)+1=sec^4(x)	prove\:\tan^{4}(x)+\tan^{2}(x)+1=\sec^{4}(x)
prove tan^3(x)-cot^3(x)=tan^2(x)sin^2(x)	prove\:\tan^{3}(x)-\cot^{3}(x)=\tan^{2}(x)\sin^{2}(x)
prove csc^2(θ)=cot^2(θ)+1	prove\:\csc^{2}(θ)=\cot^{2}(θ)+1
prove (1+tan^2(x))/(tan(x))=sec(x)csc(x)	prove\:\frac{1+\tan^{2}(x)}{\tan(x)}=\sec(x)\csc(x)
prove csc(x)sin(x)-cos^2(x)=sin^2(x)	prove\:\csc(x)\sin(x)-\cos^{2}(x)=\sin^{2}(x)
prove (tan^2(A))/(tan^2(A)+1)=sin^2(A)	prove\:\frac{\tan^{2}(A)}{\tan^{2}(A)+1}=\sin^{2}(A)
prove (sec^4(α)-1)/(tan^2(α))=sec^2(α)+1	prove\:\frac{\sec^{4}(α)-1}{\tan^{2}(α)}=\sec^{2}(α)+1
prove (1+sec(x))/(csc(x))-tan(x)=sin(x)	prove\:\frac{1+\sec(x)}{\csc(x)}-\tan(x)=\sin(x)
prove 2sin(x)=(4cos(x)-1)/(tan(x))	prove\:2\sin(x)=\frac{4\cos(x)-1}{\tan(x)}
prove cos(8x)=cos^2(4x)-sin^2(4x)	prove\:\cos(8x)=\cos^{2}(4x)-\sin^{2}(4x)
prove tan(pi/2-x)cot(x)=csc^2(x)-1	prove\:\tan(\frac{π}{2}-x)\cot(x)=\csc^{2}(x)-1
prove cot^2(θ)cos(2θ)=cot^2(θ)-2cos^2(θ)	prove\:\cot^{2}(θ)\cos(2θ)=\cot^{2}(θ)-2\cos^{2}(θ)
prove (cot^2(x))/(cos(x))=cot(x)*csc(x)	prove\:\frac{\cot^{2}(x)}{\cos(x)}=\cot(x)\cdot\:\csc(x)
prove 1-tan(x)=(cos(x)-sin(x))/(cos(x))	prove\:1-\tan(x)=\frac{\cos(x)-\sin(x)}{\cos(x)}
prove sin(2t+pi)=sin(2t)cos(pi)+cos(2t)sin(pi)	prove\:\sin(2t+π)=\sin(2t)\cos(π)+\cos(2t)\sin(π)
prove (tan(x)-1)/(sec(x))=sin(x)-cos(x)	prove\:\frac{\tan(x)-1}{\sec(x)}=\sin(x)-\cos(x)
prove cot^2(α)=cos^2(α)+(cot(α)*cos(α))^2	prove\:\cot^{2}(α)=\cos^{2}(α)+(\cot(α)\cdot\:\cos(α))^{2}
prove 1/(tan(α))*1/(cos(α))= 1/(sin(α))	prove\:\frac{1}{\tan(α)}\cdot\:\frac{1}{\cos(α)}=\frac{1}{\sin(α)}
prove (cot^2(x))/(cos^2(x))=csc^2(x)	prove\:\frac{\cot^{2}(x)}{\cos^{2}(x)}=\csc^{2}(x)
prove cos(x)-1=(cos(2x)-1)/(2(cos(x)+1))	prove\:\cos(x)-1=\frac{\cos(2x)-1}{2(\cos(x)+1)}
prove sec(x)=arccos(x)	prove\:\sec(x)=\arccos(x)
prove tan(θ)+sin(θ)=4(1+cos(θ))	prove\:\tan(θ)+\sin(θ)=4(1+\cos(θ))
prove 2/(cot(x)tan(x))=sin(2x)	prove\:\frac{2}{\cot(x)\tan(x)}=\sin(2x)
prove (sin(x)-cos(x))^2=1+sin(2x)	prove\:(\sin(x)-\cos(x))^{2}=1+\sin(2x)
prove cos^2(a)-cos^2(a)sin^2(a)=cos^4(a)	prove\:\cos^{2}(a)-\cos^{2}(a)\sin^{2}(a)=\cos^{4}(a)
prove (tan^2(x))/(sec(x)-1)=1+sec(x)	prove\:\frac{\tan^{2}(x)}{\sec(x)-1}=1+\sec(x)
prove 2sin^2(3x)+cos(6x)=1	prove\:2\sin^{2}(3x)+\cos(6x)=1
prove csc(θ)*cos(θ)=cot(θ)	prove\:\csc(θ)\cdot\:\cos(θ)=\cot(θ)
prove sinh^2(x)=cosh^2(x)-1	prove\:\sinh^{2}(x)=\cosh^{2}(x)-1
prove 4sin^2(x)+2cos^2(x)=4-2cos^2(x)	prove\:4\sin^{2}(x)+2\cos^{2}(x)=4-2\cos^{2}(x)
prove sin(x/2)*cos(x/2)= 1/2 sin(x)	prove\:\sin(\frac{x}{2})\cdot\:\cos(\frac{x}{2})=\frac{1}{2}\sin(x)
prove 2cos(4θ)+5=16sin^2(θ)	prove\:2\cos(4θ)+5=16\sin^{2}(θ)
prove (1+cos(x))(csc(x)-cot(x))=sin(x)	prove\:(1+\cos(x))(\csc(x)-\cot(x))=\sin(x)
prove cos^2(r)-1=-sin^2(r)	prove\:\cos^{2}(r)-1=-\sin^{2}(r)
prove (tan^2(θ))/(sin(θ))=sec(θ)tan(θ)	prove\:\frac{\tan^{2}(θ)}{\sin(θ)}=\sec(θ)\tan(θ)
prove (csc^2(x))/(csc^2(x)-1)=sec^2(x)	prove\:\frac{\csc^{2}(x)}{\csc^{2}(x)-1}=\sec^{2}(x)
prove sin(2x)+sin(2y)=2sin(x+y)cos(x-y)	prove\:\sin(2x)+\sin(2y)=2\sin(x+y)\cos(x-y)
prove sin(θ)csc(θ)cos(θ)=cos(θ)	prove\:\sin(θ)\csc(θ)\cos(θ)=\cos(θ)
prove cot(x)-csc^2(x)cot(x)=-cot^3(x)	prove\:\cot(x)-\csc^{2}(x)\cot(x)=-\cot^{3}(x)
prove cot(x-pi/2)=-tan(x)	prove\:\cot(x-\frac{π}{2})=-\tan(x)
prove (sin(5x)+sin(11x))/(cos(5x)+cos(11x))=tan(8x)	prove\:\frac{\sin(5x)+\sin(11x)}{\cos(5x)+\cos(11x)}=\tan(8x)
prove (sec(x)-1)/(sin(x)sec(x))=tan(x/2)	prove\:\frac{\sec(x)-1}{\sin(x)\sec(x)}=\tan(\frac{x}{2})
prove cos(4x)-sin(4x)=cos(2x)	prove\:\cos(4x)-\sin(4x)=\cos(2x)
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 (1+tan^2(θ))/(1-tan^2(θ))=sec(2θ)	prove\:\frac{1+\tan^{2}(θ)}{1-\tan^{2}(θ)}=\sec(2θ)
prove cos^2(3x)-sin^2(3x)=cos(6x)	prove\:\cos^{2}(3x)-\sin^{2}(3x)=\cos(6x)
prove sec^2(Θ)csc^2(Θ)=sec^2(Θ)+csc^2(Θ)	prove\:\sec^{2}(Θ)\csc^{2}(Θ)=\sec^{2}(Θ)+\csc^{2}(Θ)
prove (cos(t))/(1-sin(t))=sec(t)+tan(t)	prove\:\frac{\cos(t)}{1-\sin(t)}=\sec(t)+\tan(t)
prove (sec(x)-1)^4=2tan^2(x)-tan^4(x)	prove\:(\sec(x)-1)^{4}=2\tan^{2}(x)-\tan^{4}(x)
prove sin(2x)=2(cos(x))/(csc(x))	prove\:\sin(2x)=2\frac{\cos(x)}{\csc(x)}
prove 2sin(30)cos(30)=sin(60)	prove\:2\sin(30^{\circ\:})\cos(30^{\circ\:})=\sin(60^{\circ\:})
prove (cot(θ)+tan(θ))/(cot(θ))=sec^2(θ)	prove\:\frac{\cot(θ)+\tan(θ)}{\cot(θ)}=\sec^{2}(θ)
prove sin(2x)=(2sin(x))/(sec(x))	prove\:\sin(2x)=\frac{2\sin(x)}{\sec(x)}
prove 4sin^2(x)tan(x)=tan(x)	prove\:4\sin^{2}(x)\tan(x)=\tan(x)
prove sin(x)= 3/4*(sin(x))/(3/4)	prove\:\sin(x)=\frac{3}{4}\cdot\:\frac{\sin(x)}{\frac{3}{4}}
prove (tan(x)+2)=2+sec(x)sin(x)	prove\:(\tan(x)+2)=2+\sec(x)\sin(x)
prove tan(θ-45)+tan(θ+45)=2tan(2θ)	prove\:\tan(θ-45^{\circ\:})+\tan(θ+45^{\circ\:})=2\tan(2θ)
prove tan(2θ)-tan(θ)=tan(θ)sec(2θ)	prove\:\tan(2θ)-\tan(θ)=\tan(θ)\sec(2θ)
prove (sin(x))/(csc(x))=sin^2(x)	prove\:\frac{\sin(x)}{\csc(x)}=\sin^{2}(x)
prove tan(2A)-tan(A)=tan(A)sec(2A)	prove\:\tan(2A)-\tan(A)=\tan(A)\sec(2A)
prove 1/(1-csc(x))-1/(1+csc(x))=-2tan(x)sec(x)	prove\:\frac{1}{1-\csc(x)}-\frac{1}{1+\csc(x)}=-2\tan(x)\sec(x)
prove-2sin(x-y)sin(x+y)=cos(2x)-cos(2y)	prove\:-2\sin(x-y)\sin(x+y)=\cos(2x)-\cos(2y)
prove (csc^2(x))/(cot(x))=csc(x)*sec(x)	prove\:\frac{\csc^{2}(x)}{\cot(x)}=\csc(x)\cdot\:\sec(x)
prove (1-sin(x))+(1+sin(x))=2cos(x)	prove\:(1-\sin(x))+(1+\sin(x))=2\cos(x)
prove-1/(sin(x))=-csc(x)	prove\:-\frac{1}{\sin(x)}=-\csc(x)
prove tan^2(θ)+4=sec^2(θ)+3	prove\:\tan^{2}(θ)+4=\sec^{2}(θ)+3
prove (sin^2(a))/(1+cos(a))=1-cos(a)	prove\:\frac{\sin^{2}(a)}{1+\cos(a)}=1-\cos(a)
prove 1/(1-sin(β))+1/(1+sin(β))=2sec^2(β)	prove\:\frac{1}{1-\sin(β)}+\frac{1}{1+\sin(β)}=2\sec^{2}(β)

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