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Popular Trigonometry Problems

prove 2cos^2(x)-1=cos^2(x)-sin^2(x)	prove\:2\cos^{2}(x)-1=\cos^{2}(x)-\sin^{2}(x)
prove (1+tan(θ))/(1+cot(θ))=tan(θ)	prove\:\frac{1+\tan(θ)}{1+\cot(θ)}=\tan(θ)
prove cos(x+1)=cos(-x-1)	prove\:\cos(x+1)=\cos(-x-1)
prove cos(x)(tan(x)sec(x))=sin(x)-1	prove\:\cos(x)(\tan(x)\sec(x))=\sin(x)-1
prove (tan(θ))/(sin(θ))=sec(θ)	prove\:\frac{\tan(θ)}{\sin(θ)}=\sec(θ)
prove (tan(2x))/(tan(x))=1+sec(2x)	prove\:\frac{\tan(2x)}{\tan(x)}=1+\sec(2x)
prove tan(u)-sec(u)=(cos(u))/(1+sin(u))	prove\:\tan(u)-\sec(u)=\frac{\cos(u)}{1+\sin(u)}
prove cot^2(x)+1= 1/(sin^2(x))	prove\:\cot^{2}(x)+1=\frac{1}{\sin^{2}(x)}
prove cos(2θ)=cos^4(θ)-sin^4(θ)	prove\:\cos(2θ)=\cos^{4}(θ)-\sin^{4}(θ)
prove (sin(2A))/(1-cos(2A))=cot(A)	prove\:\frac{\sin(2A)}{1-\cos(2A)}=\cot(A)
prove sin(6x)=2sin(3x)cos(3x)	prove\:\sin(6x)=2\sin(3x)\cos(3x)
prove sin(4x)=4sin(x)cos(x)	prove\:\sin(4x)=4\sin(x)\cos(x)
prove (1+cot^2(θ))tan^2(θ)=sec^2(θ)	prove\:(1+\cot^{2}(θ))\tan^{2}(θ)=\sec^{2}(θ)
prove sin(a)+cos(a)=(1+tan(a))/(sec(a))	prove\:\sin(a)+\cos(a)=\frac{1+\tan(a)}{\sec(a)}
prove (cos(x))^3=cos^3(x)	prove\:(\cos(x))^{3}=\cos^{3}(x)
prove cot(θ)=sec(θ)csc(θ)-tan(θ)	prove\:\cot(θ)=\sec(θ)\csc(θ)-\tan(θ)
prove sin^2(β)csc^2(β)-sin^2(β)=cos^2(β)	prove\:\sin^{2}(β)\csc^{2}(β)-\sin^{2}(β)=\cos^{2}(β)
prove (sin(θ)+1)(sin(θ)-1)=-cos^2(θ)	prove\:(\sin(θ)+1)(\sin(θ)-1)=-\cos^{2}(θ)
prove cos(x)=sin(x)	prove\:\cos(x)=\sin(x)
prove csc(x)-cot(x)=tan(x/2)	prove\:\csc(x)-\cot(x)=\tan(\frac{x}{2})
prove cot^2(a)-cos^2(a)=cot^2(a)cos^2(a)	prove\:\cot^{2}(a)-\cos^{2}(a)=\cot^{2}(a)\cos^{2}(a)
prove (sin^2(x))/(cos(x))=tan(x)sin(x)	prove\:\frac{\sin^{2}(x)}{\cos(x)}=\tan(x)\sin(x)
prove cos^2(θ)(sec^2(θ)-1)=sin^2(θ)	prove\:\cos^{2}(θ)(\sec^{2}(θ)-1)=\sin^{2}(θ)
prove cot^2(y)sec^2(y)=1+cot^2(y)	prove\:\cot^{2}(y)\sec^{2}(y)=1+\cot^{2}(y)
prove csc(θ)-cot(θ)*cos(θ)=sin(θ)	prove\:\csc(θ)-\cot(θ)\cdot\:\cos(θ)=\sin(θ)
prove (cos(x))/(1-sin(x))=tan(x)+sec(x)	prove\:\frac{\cos(x)}{1-\sin(x)}=\tan(x)+\sec(x)
prove cot(x)+tan(x)=(sec^2(x))/(tan(x))	prove\:\cot(x)+\tan(x)=\frac{\sec^{2}(x)}{\tan(x)}
prove (sin(x+y))/(cos(x-y))=(cot(x)+cot(y))/(1+cot(x)cot(y))	prove\:\frac{\sin(x+y)}{\cos(x-y)}=\frac{\cot(x)+\cot(y)}{1+\cot(x)\cot(y)}
prove cot(x)csc(x)+sec(x)=csc^2(x)sec(x)	prove\:\cot(x)\csc(x)+\sec(x)=\csc^{2}(x)\sec(x)
prove 1/(cos(x))=sec(x)	prove\:\frac{1}{\cos(x)}=\sec(x)
prove 1/(1+cos(θ))+1/(1-cos(θ))=2csc^2(θ)	prove\:\frac{1}{1+\cos(θ)}+\frac{1}{1-\cos(θ)}=2\csc^{2}(θ)
prove (csc(A)-cot(A))(sec(A)+1)=tan(A)	prove\:(\csc(A)-\cot(A))(\sec(A)+1)=\tan(A)
prove-sin(x)=cos(pi/2+x)	prove\:-\sin(x)=\cos(\frac{π}{2}+x)
prove sin(a+b)-sin(a-b)=2cos(a)sin(b)	prove\:\sin(a+b)-\sin(a-b)=2\cos(a)\sin(b)
prove 1+cot^2(θ)= 1/(sin^2(θ))	prove\:1+\cot^{2}(θ)=\frac{1}{\sin^{2}(θ)}
prove sin(2pi-x)=-sin(x)	prove\:\sin(2π-x)=-\sin(x)
prove csc(θ)-(sin(θ))/(1+cos(θ))=cot(θ)	prove\:\csc(θ)-\frac{\sin(θ)}{1+\cos(θ)}=\cot(θ)
prove 1/(sin(x)cos(x))-cot(x)=tan(x)	prove\:\frac{1}{\sin(x)\cos(x)}-\cot(x)=\tan(x)
prove (sin^2(x)-cos^2(x)+1)/2 =sin^2(x)	prove\:\frac{\sin^{2}(x)-\cos^{2}(x)+1}{2}=\sin^{2}(x)
prove sin^2(a)+sin^2(a)tan^2(a)=tan^2(a)	prove\:\sin^{2}(a)+\sin^{2}(a)\tan^{2}(a)=\tan^{2}(a)
prove sin(b)+cos(b)cot(b)=csc(b)	prove\:\sin(b)+\cos(b)\cot(b)=\csc(b)
prove sin^2(θ)(csc^2(θ)-1)=cos^2(θ)	prove\:\sin^{2}(θ)(\csc^{2}(θ)-1)=\cos^{2}(θ)
prove cot(α)sec(α)=csc(α)	prove\:\cot(α)\sec(α)=\csc(α)
prove (sec(x)-cos(x))/(sin^2(x))=sec(x)	prove\:\frac{\sec(x)-\cos(x)}{\sin^{2}(x)}=\sec(x)
prove 1/(sec(a)+tan(a))=sec(a)-tan(a)	prove\:\frac{1}{\sec(a)+\tan(a)}=\sec(a)-\tan(a)
prove (1-cos(2x))/(2sin(x))=sin(x)	prove\:\frac{1-\cos(2x)}{2\sin(x)}=\sin(x)
prove sin^3(θ)+sin(θ)cos^2(θ)=sin(θ)	prove\:\sin^{3}(θ)+\sin(θ)\cos^{2}(θ)=\sin(θ)
prove sec^2(θ)cot^2(θ)=csc^2(θ)	prove\:\sec^{2}(θ)\cot^{2}(θ)=\csc^{2}(θ)
prove tan((3pi)/2-x)=cot(x)	prove\:\tan(\frac{3π}{2}-x)=\cot(x)
prove (3csc(-x))/(sec(-x))=-3cot(x)	prove\:\frac{3\csc(-x)}{\sec(-x)}=-3\cot(x)
prove (1-tan^4(x))/(1-tan^2(x))=sec^2(x)	prove\:\frac{1-\tan^{4}(x)}{1-\tan^{2}(x)}=\sec^{2}(x)
prove (sin(x))/(1+cos(x))=tan(x/2)	prove\:\frac{\sin(x)}{1+\cos(x)}=\tan(\frac{x}{2})
prove cos(4x)=1-2sin^2(2x)	prove\:\cos(4x)=1-2\sin^{2}(2x)
prove cos(pi-x)+sin(pi/2+x)=0	prove\:\cos(π-x)+\sin(\frac{π}{2}+x)=0
prove cot^2(x)csc^2(x)-cot^2(x)=cot^4(x)	prove\:\cot^{2}(x)\csc^{2}(x)-\cot^{2}(x)=\cot^{4}(x)
prove arcsin(x)=csc(x)	prove\:\arcsin(x)=\csc(x)
prove 1/(tan(x)csc(x)sin(x))=cot(x)	prove\:\frac{1}{\tan(x)\csc(x)\sin(x)}=\cot(x)
prove (1-sin(x))(1+csc(x))=cos(x)cot(x)	prove\:(1-\sin(x))(1+\csc(x))=\cos(x)\cot(x)
prove 1/(cos(x))=(tan(x))/(sin(x))	prove\:\frac{1}{\cos(x)}=\frac{\tan(x)}{\sin(x)}
prove cos^4(A)-sin^4(A)=cos(2A)	prove\:\cos^{4}(A)-\sin^{4}(A)=\cos(2A)
prove cos(θ)(csc(θ)-sec(θ))=cot(θ)-1	prove\:\cos(θ)(\csc(θ)-\sec(θ))=\cot(θ)-1
prove tan^4(x)-sec^4(x)=1-2sec^2(x)	prove\:\tan^{4}(x)-\sec^{4}(x)=1-2\sec^{2}(x)
prove 3sin^2(x)-9sin(x)cot(x)+7cos^2(x)-4cos(x)=(4cos(x)-1)(cos(x)-3)	prove\:3\sin^{2}(x)-9\sin(x)\cot(x)+7\cos^{2}(x)-4\cos(x)=(4\cos(x)-1)(\cos(x)-3)
prove csc(x)+1=(cot(x))/(sec(x)-tan(x))	prove\:\csc(x)+1=\frac{\cot(x)}{\sec(x)-\tan(x)}
prove sin(x)sec^2(x)=(tan(x))/(cos(x))	prove\:\sin(x)\sec^{2}(x)=\frac{\tan(x)}{\cos(x)}
prove (1+sec^2(x))/(sec^2(x))=1+cos^2(x)	prove\:\frac{1+\sec^{2}(x)}{\sec^{2}(x)}=1+\cos^{2}(x)
prove sin(2θ)=2cot(θ)sin^2(θ)	prove\:\sin(2θ)=2\cot(θ)\sin^{2}(θ)
prove tan(θ)+1=sec(θ)	prove\:\tan(θ)+1=\sec(θ)
prove (sec^2(x)-1)/(sin(x))=tan(x)sec(x)	prove\:\frac{\sec^{2}(x)-1}{\sin(x)}=\tan(x)\sec(x)
prove cos(θ)-cos^3(θ)=sin^2(θ)cos(θ)	prove\:\cos(θ)-\cos^{3}(θ)=\sin^{2}(θ)\cos(θ)
prove (cos(4x)+1)/(sin(4x))=cot(2x)	prove\:\frac{\cos(4x)+1}{\sin(4x)}=\cot(2x)
prove 2sin(θ)cos(θ)=tan(2θ)cos(2θ)	prove\:2\sin(θ)\cos(θ)=\tan(2θ)\cos(2θ)
prove cos(θ)sec(θ)-cos^2(θ)=sin^2(θ)	prove\:\cos(θ)\sec(θ)-\cos^{2}(θ)=\sin^{2}(θ)
prove sin(12x)=2sin(6x)cos(6x)	prove\:\sin(12x)=2\sin(6x)\cos(6x)
prove (sin(t))/(csc(t))=1-(cos(t))/(sec(t))	prove\:\frac{\sin(t)}{\csc(t)}=1-\frac{\cos(t)}{\sec(t)}
prove cot^2(x)=1-csc^2(x)	prove\:\cot^{2}(x)=1-\csc^{2}(x)
prove tan^4(θ)=tan^2(θ)sec^2(θ)-tan^2(θ)	prove\:\tan^{4}(θ)=\tan^{2}(θ)\sec^{2}(θ)-\tan^{2}(θ)
prove (sin(6A)+sin(2A))/(cos(6A)-cos(2A))=-cot(2A)	prove\:\frac{\sin(6A)+\sin(2A)}{\cos(6A)-\cos(2A)}=-\cot(2A)
prove 1+cos(θ)=(sin^2(θ))/(1-cos(θ))	prove\:1+\cos(θ)=\frac{\sin^{2}(θ)}{1-\cos(θ)}
prove cot(x)-sin(2x)=cot(x)cos(2x)	prove\:\cot(x)-\sin(2x)=\cot(x)\cos(2x)
prove sin(2θ)=2sin(2θ)cos(2θ)	prove\:\sin(2θ)=2\sin(2θ)\cos(2θ)
prove 1+(cos^2(θ))/(1+sin(θ))=sin(θ)	prove\:1+\frac{\cos^{2}(θ)}{1+\sin(θ)}=\sin(θ)
prove (cos(2x))/(cos^2(x))=2-sec^2(x)	prove\:\frac{\cos(2x)}{\cos^{2}(x)}=2-\sec^{2}(x)
prove 1/(cos(θ))-cos(θ)=sin(θ)tan(θ)	prove\:\frac{1}{\cos(θ)}-\cos(θ)=\sin(θ)\tan(θ)
prove sec^2(2x)-tan^2(2x)=1	prove\:\sec^{2}(2x)-\tan^{2}(2x)=1
prove cot^2(x)(1-cos^2(x))=cos^2(x)	prove\:\cot^{2}(x)(1-\cos^{2}(x))=\cos^{2}(x)
prove sec^2(θ)=1+tan^2(θ)	prove\:\sec^{2}(θ)=1+\tan^{2}(θ)
prove 1+tan^2(30)=sec^2(30)	prove\:1+\tan^{2}(30^{\circ\:})=\sec^{2}(30^{\circ\:})
prove (sin(x))^2-(sec(x))(sin(x))^3=-1	prove\:(\sin(x))^{2}-(\sec(x))(\sin(x))^{3}=-1
prove sin(2x)(tan(x)+cot(x))=2	prove\:\sin(2x)(\tan(x)+\cot(x))=2
prove sec^4(x)-tan^4(x)=2sec^2(x)-1	prove\:\sec^{4}(x)-\tan^{4}(x)=2\sec^{2}(x)-1
prove (cos(θ)+sin(θ))/(cos(θ))=1+tan(θ)	prove\:\frac{\cos(θ)+\sin(θ)}{\cos(θ)}=1+\tan(θ)
prove sin(2x)=cot(x)(1-cos(2x))	prove\:\sin(2x)=\cot(x)(1-\cos(2x))
prove (cos(θ))/(1-sin(θ))-tan(θ)=sec(θ)	prove\:\frac{\cos(θ)}{1-\sin(θ)}-\tan(θ)=\sec(θ)
prove sec(x)csc(x)=(sec^2(x))/(tan(x))	prove\:\sec(x)\csc(x)=\frac{\sec^{2}(x)}{\tan(x)}
prove sin^2(θ)sec(θ)csc(θ)=tan(θ)	prove\:\sin^{2}(θ)\sec(θ)\csc(θ)=\tan(θ)
prove 6cot^2(y)(sec^2(y)-1)=6	prove\:6\cot^{2}(y)(\sec^{2}(y)-1)=6
prove csc(x)(cos(x)+sin(x))=cot(x)+1	prove\:\csc(x)(\cos(x)+\sin(x))=\cot(x)+1
prove cos^2(x)+cos^2(x)cot^2(x)=cot^2(x)	prove\:\cos^{2}(x)+\cos^{2}(x)\cot^{2}(x)=\cot^{2}(x)
prove (1-cos^4(x))/(sin^2(x))=1+cos^2(x)	prove\:\frac{1-\cos^{4}(x)}{\sin^{2}(x)}=1+\cos^{2}(x)

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