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Popular Trigonometry Problems

prove sec(x)*cot(x)=csc(x)	prove\:\sec(x)\cdot\:\cot(x)=\csc(x)
prove (tan^2(x))/(sec(t))=sec(t)-cos(t)	prove\:\frac{\tan^{2}(x)}{\sec(t)}=\sec(t)-\cos(t)
prove (cot(x)+1)/(sin(x)+cos(x))=csc(x)	prove\:\frac{\cot(x)+1}{\sin(x)+\cos(x)}=\csc(x)
prove sec(A)csc(A)=tan(A)cot(A)	prove\:\sec(A)\csc(A)=\tan(A)\cot(A)
prove (1-cos(2x))/2 =1-cos^2(x)	prove\:\frac{1-\cos(2x)}{2}=1-\cos^{2}(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 ((-sin^2(a)+1))/(cos(a))=cos(a)	prove\:\frac{(-\sin^{2}(a)+1)}{\cos(a)}=\cos(a)
prove 2csc(2x)tan(x)=sec^2(x)	prove\:2\csc(2x)\tan(x)=\sec^{2}(x)
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 ((sin(a)+sin(3a)))/(cos(a)+cos(3a))=tan(2a)	prove\:\frac{(\sin(a)+\sin(3a))}{\cos(a)+\cos(3a)}=\tan(2a)
prove 4sec^2(θ)-3=1+4tan^2(θ)	prove\:4\sec^{2}(θ)-3=1+4\tan^{2}(θ)
prove sec(θ)=csc(θ)tan(θ)	prove\:\sec(θ)=\csc(θ)\tan(θ)
prove-sin(x)=sin(x)	prove\:-\sin(x)=\sin(x)
prove (csc^2(x)+1)/(cot^2(x))=(1+sin^2(x))/(cos^2(x))	prove\:\frac{\csc^{2}(x)+1}{\cot^{2}(x)}=\frac{1+\sin^{2}(x)}{\cos^{2}(x)}
prove sec(x)+tan(x)=(1/(sec(x)-tan(x)))	prove\:\sec(x)+\tan(x)=(\frac{1}{\sec(x)-\tan(x)})
prove (sec(a)-tan(a))(sec(a)+tan(a))=1	prove\:(\sec(a)-\tan(a))(\sec(a)+\tan(a))=1
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 tan(x)(1-csc^2(x))=-cot(x)	prove\:\tan(x)(1-\csc^{2}(x))=-\cot(x)
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 2cos^2(x)=2cos(x)cos(x)	prove\:2\cos^{2}(x)=2\cos(x)\cos(x)
prove 1/(cos(θ)sin(θ))=sec(θ)csc(θ)	prove\:\frac{1}{\cos(θ)\sin(θ)}=\sec(θ)\csc(θ)
prove csc(pi/(2-x))cot(x)=csc(x)	prove\:\csc(\frac{π}{2-x})\cot(x)=\csc(x)
prove (csc(x)+sec(x))/(1+tan(x))=csc(x)	prove\:\frac{\csc(x)+\sec(x)}{1+\tan(x)}=\csc(x)
prove (3)((cos^2(2z)))/2 =(3cos(4z))/4	prove\:(3)\frac{(\cos^{2}(2z))}{2}=\frac{3\cos(4z)}{4}
prove cos^2(x)(cot^2(x)+1)=cot^2(x)	prove\:\cos^{2}(x)(\cot^{2}(x)+1)=\cot^{2}(x)
prove sin(pi/6+x)=cos(pi/3-x)	prove\:\sin(\frac{π}{6}+x)=\cos(\frac{π}{3}-x)
prove 2cos^2(x)-1=0	prove\:2\cos^{2}(x)-1=0
prove (1+cos(2θ))(1-cos(2θ))=sin^2(2θ)	prove\:(1+\cos(2θ))(1-\cos(2θ))=\sin^{2}(2θ)
prove sin(x)-cos(x)=0	prove\:\sin(x)-\cos(x)=0
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 (tan^4(x)-1)/(tan^2(x)-1)=sec^2(x)	prove\:\frac{\tan^{4}(x)-1}{\tan^{2}(x)-1}=\sec^{2}(x)
prove csc(β)-csc(β)cos(2β)=2*sin(β)	prove\:\csc(β)-\csc(β)\cos(2β)=2\cdot\:\sin(β)
prove cos(270-θ)=-sin(θ)	prove\:\cos(270^{\circ\:}-θ)=-\sin(θ)
prove 1-cos^2(x)tan^2(x)=cos^2(x)	prove\:1-\cos^{2}(x)\tan^{2}(x)=\cos^{2}(x)
prove cot(2a)= 1/2 (cot(a)-tan(a))	prove\:\cot(2a)=\frac{1}{2}(\cot(a)-\tan(a))
prove sec(t)=(cot(t)+tan(t))/(csc(t))	prove\:\sec(t)=\frac{\cot(t)+\tan(t)}{\csc(t)}
prove (1-cos(2a))/(sin(2a))=tan(a)	prove\:\frac{1-\cos(2a)}{\sin(2a)}=\tan(a)
prove sin(2x)+sin(x)=sin(3x)	prove\:\sin(2x)+\sin(x)=\sin(3x)
prove tan^2(x)= 1/(cot^2(x))	prove\:\tan^{2}(x)=\frac{1}{\cot^{2}(x)}
prove-sin^2(x)+cos^2(x)=0	prove\:-\sin^{2}(x)+\cos^{2}(x)=0
prove 1/(1-sin(t))=sec^2(t)+sec(t)tan(t)	prove\:\frac{1}{1-\sin(t)}=\sec^{2}(t)+\sec(t)\tan(t)
prove sec(x)cos(-x)-sin^2(x)=cos^2(x)	prove\:\sec(x)\cos(-x)-\sin^{2}(x)=\cos^{2}(x)
prove sec^2(x)cos(x)-sec(x)=0	prove\:\sec^{2}(x)\cos(x)-\sec(x)=0
prove sin^4(x)=(1-cos^2(x))^2	prove\:\sin^{4}(x)=(1-\cos^{2}(x))^{2}
prove sec(z)cot(z)sin(z)=1	prove\:\sec(z)\cot(z)\sin(z)=1
prove cos(θ)= 2/3	prove\:\cos(θ)=\frac{2}{3}
prove cos(4x)+sin(4x)=cos(2x)	prove\:\cos(4x)+\sin(4x)=\cos(2x)
prove (sec(x)-1)/(sec(x))=2sin^2(x/2)	prove\:\frac{\sec(x)-1}{\sec(x)}=2\sin^{2}(\frac{x}{2})
prove sin(2pi-B)=-sin(B)	prove\:\sin(2π-B)=-\sin(B)
prove sin^3(x)=sin^2(x)sin(x)	prove\:\sin^{3}(x)=\sin^{2}(x)\sin(x)
prove (cos^2(a))/(1+sin(a))=1-sin(a)	prove\:\frac{\cos^{2}(a)}{1+\sin(a)}=1-\sin(a)
prove sin^2(α)sec(α)=tan^2(α)	prove\:\sin^{2}(α)\sec(α)=\tan^{2}(α)
prove 1+tan(2x)tan(x)=sec(2x)	prove\:1+\tan(2x)\tan(x)=\sec(2x)
prove 4/(cos^2(x))-5=4tan^2(x)-1	prove\:\frac{4}{\cos^{2}(x)}-5=4\tan^{2}(x)-1
prove (sec(x)+tan(x))(1-sec(x))=cos(x)	prove\:(\sec(x)+\tan(x))(1-\sec(x))=\cos(x)
prove tan(x)cos(2x)=sin(2x)-tan(x)	prove\:\tan(x)\cos(2x)=\sin(2x)-\tan(x)
prove (sin^2(θ))/(tan^2(θ))=cos^2(θ)	prove\:\frac{\sin^{2}(θ)}{\tan^{2}(θ)}=\cos^{2}(θ)
prove sin(x)+sin(y)=2sin((x+y)/2)cos((x-y)/2)	prove\:\sin(x)+\sin(y)=2\sin(\frac{x+y}{2})\cos(\frac{x-y}{2})
prove sec^2(θ)-2tan(θ)=(tan(θ)-1)^2	prove\:\sec^{2}(θ)-2\tan(θ)=(\tan(θ)-1)^{2}
prove 1/(csc(x))+1=sin(x)+1	prove\:\frac{1}{\csc(x)}+1=\sin(x)+1
prove 25sin^2(x)+25cos^2(x)=25	prove\:25\sin^{2}(x)+25\cos^{2}(x)=25
prove cot(x)sin(x)sec(x)=1	prove\:\cot(x)\sin(x)\sec(x)=1
prove 1/(1-cos(x))-1/(1+cos(x))=2cot(x)csc(x)	prove\:\frac{1}{1-\cos(x)}-\frac{1}{1+\cos(x)}=2\cot(x)\csc(x)
prove tan^2(x)-sec^2(x)=1	prove\:\tan^{2}(x)-\sec^{2}(x)=1
prove tan(x)sin(x)=(sin^2(x))/(cos(x))	prove\:\tan(x)\sin(x)=\frac{\sin^{2}(x)}{\cos(x)}
prove tan^2(t)= 1/(cos^2(t))-1	prove\:\tan^{2}(t)=\frac{1}{\cos^{2}(t)}-1
prove (2sin(x)cos(x))^4=sin^4(2x)	prove\:(2\sin(x)\cos(x))^{4}=\sin^{4}(2x)
prove (1+cot^2(x))sin^2(x)=1	prove\:(1+\cot^{2}(x))\sin^{2}(x)=1
prove csc(θ)+sec(θ)=tan(θ)+1	prove\:\csc(θ)+\sec(θ)=\tan(θ)+1
prove (cos(t)+1)/(sin(t)+sec(t))=(tan(t))/(sec(t)-1)	prove\:\frac{\cos(t)+1}{\sin(t)+\sec(t)}=\frac{\tan(t)}{\sec(t)-1}
prove (cot(θ)-tan(θ))/(cot(θ)+tan(θ))=cos(2θ)	prove\:\frac{\cot(θ)-\tan(θ)}{\cot(θ)+\tan(θ)}=\cos(2θ)
prove cos^2(2x)+4sin^2(x)cos^2(x)=1	prove\:\cos^{2}(2x)+4\sin^{2}(x)\cos^{2}(x)=1
prove cos(x)(sec(x)-1)=1-cos(x)	prove\:\cos(x)(\sec(x)-1)=1-\cos(x)
prove 3sec^2(330)tan(330)=4tan(330)	prove\:3\sec^{2}(330^{\circ\:})\tan(330^{\circ\:})=4\tan(330^{\circ\:})
prove (sin(x))(cot(x))=(cos(x))	prove\:(\sin(x))(\cot(x))=(\cos(x))
prove-2sin(x)cos(x)=-sin(2x)	prove\:-2\sin(x)\cos(x)=-\sin(2x)
prove cos^2(θ)cot^2(θ)=cot^2(θ)-cos^2(θ)	prove\:\cos^{2}(θ)\cot^{2}(θ)=\cot^{2}(θ)-\cos^{2}(θ)
prove csc^2(θ)(1-cos^2(θ))=-cos(pi/2)	prove\:\csc^{2}(θ)(1-\cos^{2}(θ))=-\cos(\frac{π}{2})
prove 1/2 (1-cos(2x))=sin^2(x)	prove\:\frac{1}{2}(1-\cos(2x))=\sin^{2}(x)
prove csc^2(x)tan^2(x)= 1/(cos^2(x))	prove\:\csc^{2}(x)\tan^{2}(x)=\frac{1}{\cos^{2}(x)}
prove (tan(x))/(sin(x)cos(x))=tan^2(x)+1	prove\:\frac{\tan(x)}{\sin(x)\cos(x)}=\tan^{2}(x)+1
prove cos(θ)=2cos^2(θ/2)-1	prove\:\cos(θ)=2\cos^{2}(\frac{θ}{2})-1
prove 1-sin^2(u)=cos^2(u)	prove\:1-\sin^{2}(u)=\cos^{2}(u)
prove cos(4x)=1-8cos^2(x)+8cos^4(x)	prove\:\cos(4x)=1-8\cos^{2}(x)+8\cos^{4}(x)
prove cot(x)+tan(x)= 1/(sin(x)cos(x))	prove\:\cot(x)+\tan(x)=\frac{1}{\sin(x)\cos(x)}
prove (1-sin(x))(1+sin(x))= 1/(sec^2(x))	prove\:(1-\sin(x))(1+\sin(x))=\frac{1}{\sec^{2}(x)}
prove (csc(θ)+sec(θ))/(tan(+1))=csc(θ)	prove\:\frac{\csc(θ)+\sec(θ)}{\tan(+1)}=\csc(θ)
prove (csc(x))/(csc(2x))=2cos(x)	prove\:\frac{\csc(x)}{\csc(2x)}=2\cos(x)
prove-sin(2x)=(-2cot(x))/(1+cot^2(x))	prove\:-\sin(2x)=\frac{-2\cot(x)}{1+\cot^{2}(x)}
prove 1/(cot(x))=(sin(x))/(cos(x))	prove\:\frac{1}{\cot(x)}=\frac{\sin(x)}{\cos(x)}
prove cot(x)-1=cos(x)(csc(x)-sec(x))	prove\:\cot(x)-1=\cos(x)(\csc(x)-\sec(x))
prove (1-tan^2(θ))/(cot^2(θ)-1)=tan^2(θ)	prove\:\frac{1-\tan^{2}(θ)}{\cot^{2}(θ)-1}=\tan^{2}(θ)
prove (1+tan^2(θ))/(csc(θ))=tan(θ)sec(θ)	prove\:\frac{1+\tan^{2}(θ)}{\csc(θ)}=\tan(θ)\sec(θ)
prove sec^2(x)=sin^2(x)+cos^2(x)	prove\:\sec^{2}(x)=\sin^{2}(x)+\cos^{2}(x)
prove 4sin^2(x)+4cos^2(x)=4	prove\:4\sin^{2}(x)+4\cos^{2}(x)=4

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