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Popular Trigonometry Problems

prove sec^2(θ)-cos^2(θ)=tan(θ)sin(θ)	prove\:\sec^{2}(θ)-\cos^{2}(θ)=\tan(θ)\sin(θ)
prove 1/(sec(θ)-tan(θ))=sec(θ)tan(θ)	prove\:\frac{1}{\sec(θ)-\tan(θ)}=\sec(θ)\tan(θ)
prove 1+(cos^2(x))/(1+sin(x))=sin^2(x)	prove\:1+\frac{\cos^{2}(x)}{1+\sin(x)}=\sin^{2}(x)
prove 16((1-cos(2θ))/2)=8-8cos(2θ)	prove\:16(\frac{1-\cos(2θ)}{2})=8-8\cos(2θ)
prove cot(θ)sin(θ)cos(θ)=cos^2(θ)	prove\:\cot(θ)\sin(θ)\cos(θ)=\cos^{2}(θ)
prove sec(x)+tan(x)=(sin(x)+1)/(cos(x))	prove\:\sec(x)+\tan(x)=\frac{\sin(x)+1}{\cos(x)}
prove 1-2/(1+cot^2(x))=cos(2x)	prove\:1-\frac{2}{1+\cot^{2}(x)}=\cos(2x)
prove tan(x)-1=cot(x)	prove\:\tan(x)-1=\cot(x)
prove sin^2(x)=(sec(x)sin(x))/(tan(x)+cot(x))	prove\:\sin^{2}(x)=\frac{\sec(x)\sin(x)}{\tan(x)+\cot(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 cot(A)=(cos(A))/(sin(A))	prove\:\cot(A)=\frac{\cos(A)}{\sin(A)}
prove-cot^2(x)sec^2(x)=-1-cot^2(x)	prove\:-\cot^{2}(x)\sec^{2}(x)=-1-\cot^{2}(x)
prove (cos^2(x)+1)(sec^2(x))=tan^2(x)+2	prove\:(\cos^{2}(x)+1)(\sec^{2}(x))=\tan^{2}(x)+2
prove 3-3(cos(x)-sin(x))^2=-3sin(2x)	prove\:3-3(\cos(x)-\sin(x))^{2}=-3\sin(2x)
prove (cot(T)-tan(T))/(sin(T)+cos(T))=csc(T)-sec(T)	prove\:\frac{\cot(T)-\tan(T)}{\sin(T)+\cos(T)}=\csc(T)-\sec(T)
prove csc(pi/2-x)cos(x)=1	prove\:\csc(\frac{π}{2}-x)\cos(x)=1
prove 1-2cos^2(4)=2sin^2(4)-1	prove\:1-2\cos^{2}(4)=2\sin^{2}(4)-1
prove (tan(θ))/(cot(θ)+tan(θ))=sin^2(θ)	prove\:\frac{\tan(θ)}{\cot(θ)+\tan(θ)}=\sin^{2}(θ)
prove 2sin(x)+(2+sqrt(2))=-sqrt(2)csc(x)	prove\:2\sin(x)+(2+\sqrt{2})=-\sqrt{2}\csc(x)
prove sin(8a)=4sin(2a)cos(2a)cos(4a)	prove\:\sin(8a)=4\sin(2a)\cos(2a)\cos(4a)
prove sin^2(2x)= 1/(2(1-cos^4(x)))	prove\:\sin^{2}(2x)=\frac{1}{2(1-\cos^{4}(x))}
prove ((1-sin(a)))/(cos(a))=cos(a)	prove\:\frac{(1-\sin(a))}{\cos(a)}=\cos(a)
prove csc^2(x)(tan(x))-(tan(x))=cot(x)	prove\:\csc^{2}(x)(\tan(x))-(\tan(x))=\cot(x)
prove sin^4(t)-cos^4(t)=1-2cos^2(x)	prove\:\sin^{4}(t)-\cos^{4}(t)=1-2\cos^{2}(x)
prove csc^2(A)=1+tan^2(A)	prove\:\csc^{2}(A)=1+\tan^{2}(A)
prove 3tan^2(x)=3(tan(x))^2	prove\:3\tan^{2}(x)=3(\tan(x))^{2}
prove 3cos(θ)=sqrt(3)sin(-θ)	prove\:3\cos(θ)=\sqrt{3}\sin(-θ)
prove csc^2(θ)*tan^2(θ)-1=tan^2(θ)	prove\:\csc^{2}(θ)\cdot\:\tan^{2}(θ)-1=\tan^{2}(θ)
prove tan(a)+sec(a)=(1+sin(a))/(cos(a))	prove\:\tan(a)+\sec(a)=\frac{1+\sin(a)}{\cos(a)}
prove (sin(3a))/(sin(a))=2cos(2a)+1	prove\:\frac{\sin(3a)}{\sin(a)}=2\cos(2a)+1
prove 1/(sin(x)cos(x))=(sec(x))/(sin(x))	prove\:\frac{1}{\sin(x)\cos(x)}=\frac{\sec(x)}{\sin(x)}
prove sin(2x)+cos(2x)=1+2sin(x)cos(x)	prove\:\sin(2x)+\cos(2x)=1+2\sin(x)\cos(x)
prove (cot^2(x)+1)/(cot^2(x)-1)=sec(2x)	prove\:\frac{\cot^{2}(x)+1}{\cot^{2}(x)-1}=\sec(2x)
prove-(3)(sin^2(2z))/2 =(3cos(4z))/4	prove\:-(3)\frac{\sin^{2}(2z)}{2}=\frac{3\cos(4z)}{4}
prove cot(-x)sin(-x)=cos(x)	prove\:\cot(-x)\sin(-x)=\cos(x)
prove tan((7u)/2)=csc(7u)-cot(7u)	prove\:\tan(\frac{7u}{2})=\csc(7u)-\cot(7u)
prove (sin(x)+cos(x))2=2cos(x)sin(x)+1	prove\:(\sin(x)+\cos(x))2=2\cos(x)\sin(x)+1
prove (sin(x))/1+1/(sin(x))=2csc(x)	prove\:\frac{\sin(x)}{1}+\frac{1}{\sin(x)}=2\csc(x)
prove (sin(x)+1)^2+cos^2(x)=2	prove\:(\sin(x)+1)^{2}+\cos^{2}(x)=2
prove csc(x)sec(x)cot(x)=csc^2(x)	prove\:\csc(x)\sec(x)\cot(x)=\csc^{2}(x)
prove (csc(x))/(1+tan(x))=cot^2(x)	prove\:\frac{\csc(x)}{1+\tan(x)}=\cot^{2}(x)
prove sin^2(x)=tan^2(x)+1	prove\:\sin^{2}(x)=\tan^{2}(x)+1
prove 1/(cot(x)+1)=(tan(x))/(tan(x)+1)	prove\:\frac{1}{\cot(x)+1}=\frac{\tan(x)}{\tan(x)+1}
prove (csc^2(θ))/(csc^2(θ)-2)=sec(2θ)	prove\:\frac{\csc^{2}(θ)}{\csc^{2}(θ)-2}=\sec(2θ)
prove cos^2(u)= 1/2+1/2 cos(2u)	prove\:\cos^{2}(u)=\frac{1}{2}+\frac{1}{2}\cos(2u)
prove 2sin(-y)cos(x)=2sin(-y)cos(x)	prove\:2\sin(-y)\cos(x)=2\sin(-y)\cos(x)
prove cos(θ)=sec(θ)-(tan^2(θ))/(sec(θ))	prove\:\cos(θ)=\sec(θ)-\frac{\tan^{2}(θ)}{\sec(θ)}
prove csc(x^2)sec(x^2)=csc(x^2)+sec(x^2)	prove\:\csc(x^{2})\sec(x^{2})=\csc(x^{2})+\sec(x^{2})
prove tan(θ/2)=csc^2(θ)-cot^2(θ)	prove\:\tan(\frac{θ}{2})=\csc^{2}(θ)-\cot^{2}(θ)
prove 4+4cos(2x)=8cos^2(x)	prove\:4+4\cos(2x)=8\cos^{2}(x)
prove (sec(θ)csc(θ))/2 =csc(2θ)	prove\:\frac{\sec(θ)\csc(θ)}{2}=\csc(2θ)
prove (cos(x))/(cot(x)sin(x))=1	prove\:\frac{\cos(x)}{\cot(x)\sin(x)}=1
prove (1+cos(θ))/(csc(θ))=sin(θ)+cos(θ)	prove\:\frac{1+\cos(θ)}{\csc(θ)}=\sin(θ)+\cos(θ)
prove sin^2(x)+2cos^2(x)=1+cos^2(x)	prove\:\sin^{2}(x)+2\cos^{2}(x)=1+\cos^{2}(x)
prove sin(2θ)=2cos(θ)*sin(θ)	prove\:\sin(2θ)=2\cos(θ)\cdot\:\sin(θ)
prove (1+cos(a))/(sin(a))=cot(a/2)	prove\:\frac{1+\cos(a)}{\sin(a)}=\cot(\frac{a}{2})
prove csc(θ)sin(θ)=-8/43	prove\:\csc(θ)\sin(θ)=-\frac{8}{43}
prove csc(θ)sin(θ)-sin^2(θ)=cos^2(θ)	prove\:\csc(θ)\sin(θ)-\sin^{2}(θ)=\cos^{2}(θ)
prove sin(pi/2+x)=-cos(x)	prove\:\sin(\frac{π}{2}+x)=-\cos(x)
prove tan^2(x)-sec(x)=1	prove\:\tan^{2}(x)-\sec(x)=1
prove 3cot^2(y)(sec^2(y)-1)=3	prove\:3\cot^{2}(y)(\sec^{2}(y)-1)=3
prove 2sin(pi)=5sin(pi)	prove\:2\sin(π)=5\sin(π)
prove tan(x)-1/(tan(x))=2sin^2(x)-1	prove\:\tan(x)-\frac{1}{\tan(x)}=2\sin^{2}(x)-1
prove 1/(cot(u))=(cot(u))/1	prove\:\frac{1}{\cot(u)}=\frac{\cot(u)}{1}
prove sin^2(x)*sec(x)=tan^2(x)	prove\:\sin^{2}(x)\cdot\:\sec(x)=\tan^{2}(x)
prove 1+2sin(x)cos(x)=(sin(x)+cos(x))^2	prove\:1+2\sin(x)\cos(x)=(\sin(x)+\cos(x))^{2}
prove sin(2x)=2cos(x)	prove\:\sin(2x)=2\cos(x)
prove sec(β)sin(β)cot(β)=1	prove\:\sec(β)\sin(β)\cot(β)=1
prove 1-sin^2(θ)+sin^4(θ)=cos^4(θ)	prove\:1-\sin^{2}(θ)+\sin^{4}(θ)=\cos^{4}(θ)
prove sec(x)-tan(x)=(cos^2(x))/(sin(x))	prove\:\sec(x)-\tan(x)=\frac{\cos^{2}(x)}{\sin(x)}
prove 3-6sin^2(x)=-3cos(2x)	prove\:3-6\sin^{2}(x)=-3\cos(2x)
prove (sin((5*pi/3)/4))=(sin(5 pi/(12)))	prove\:(\sin(\frac{5\cdot\:\frac{π}{3}}{4}))=(\sin(5\frac{π}{12}))
prove tan((5pi)/(12))=tan(pi/4+pi/6)	prove\:\tan(\frac{5π}{12})=\tan(\frac{π}{4}+\frac{π}{6})
prove sin^2(θ)=csc^2(θ)	prove\:\sin^{2}(θ)=\csc^{2}(θ)
prove tan(x)(sec^2(x)-1)=tan^3(x)	prove\:\tan(x)(\sec^{2}(x)-1)=\tan^{3}(x)
prove sin(x)=-1	prove\:\sin(x)=-1
prove sec(b)+tan(b)=(cos(b))/(1-sin(x))	prove\:\sec(b)+\tan(b)=\frac{\cos(b)}{1-\sin(x)}
prove 2sinh(ln(x))+(1^2)/2-4/3 =2	prove\:2\sinh(\ln(x))+\frac{1^{2}}{2}-\frac{4}{3}=2
prove 2cot^2(x)sin^2(x)=1+cos(2x)	prove\:2\cot^{2}(x)\sin^{2}(x)=1+\cos(2x)
prove 1/(tan(x))-tan(x)=2cot(2x)	prove\:\frac{1}{\tan(x)}-\tan(x)=2\cot(2x)
prove sec(x)+1=(sin(x)tan(x))/(1-cos(x))	prove\:\sec(x)+1=\frac{\sin(x)\tan(x)}{1-\cos(x)}
prove tan(u)+cos(2u)*tan(u)=sin(2u)	prove\:\tan(u)+\cos(2u)\cdot\:\tan(u)=\sin(2u)
prove (csc^2(θ)-1)/(csc^2(θ))=cos^2(θ)	prove\:\frac{\csc^{2}(θ)-1}{\csc^{2}(θ)}=\cos^{2}(θ)
prove 1+cos(x)*sin(x)=sin(x)	prove\:1+\cos(x)\cdot\:\sin(x)=\sin(x)
prove (sin(x)) 1/(sin(x))=1	prove\:(\sin(x))\frac{1}{\sin(x)}=1
prove cos(x)=(cot(x))/(csc(x)-sin(x))	prove\:\cos(x)=\frac{\cot(x)}{\csc(x)-\sin(x)}
prove cos^2(2x)=((1+cos(4x)))/2	prove\:\cos^{2}(2x)=\frac{(1+\cos(4x))}{2}
prove (1+sin(x))/(cos(x)tan(x)-1)=-1	prove\:\frac{1+\sin(x)}{\cos(x)\tan(x)-1}=-1
prove (sin(x)sec(x))/(tan(x))=1	prove\:\frac{\sin(x)\sec(x)}{\tan(x)}=1
prove cot(x)+5=5+csc(x)*cos(x)	prove\:\cot(x)+5=5+\csc(x)\cdot\:\cos(x)
prove csc(θ)=cos(θ)cot(θ)+sin^2(θ)csc(θ)	prove\:\csc(θ)=\cos(θ)\cot(θ)+\sin^{2}(θ)\csc(θ)
prove cos(y)csc(y)=cot(y)	prove\:\cos(y)\csc(y)=\cot(y)
prove (tan(a))/(sin(a))-sec(a)=0	prove\:\frac{\tan(a)}{\sin(a)}-\sec(a)=0
prove 1/(cot(θ))=(tan(θ))/(sin(θ))	prove\:\frac{1}{\cot(θ)}=\frac{\tan(θ)}{\sin(θ)}
prove (1+sin(θ))/(cos(θ))=sec(θ)+cot(θ)	prove\:\frac{1+\sin(θ)}{\cos(θ)}=\sec(θ)+\cot(θ)
prove 2cos(θ)= 2/(sec(θ))	prove\:2\cos(θ)=\frac{2}{\sec(θ)}
prove (1+sin(θ))(1-sin(θ))=cos^2(x)	prove\:(1+\sin(θ))(1-\sin(θ))=\cos^{2}(x)
prove sin^2(θ)=csc(θ)	prove\:\sin^{2}(θ)=\csc(θ)
prove (1-cot(a))/(csc(a))=sin(a)-cos(a)	prove\:\frac{1-\cot(a)}{\csc(a)}=\sin(a)-\cos(a)
prove 1/(tan^2(x)+1)+1/(cot^2(x)+1)=1	prove\:\frac{1}{\tan^{2}(x)+1}+\frac{1}{\cot^{2}(x)+1}=1

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