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Popular Trigonometry Problems

prove tan(a)cot(a)=cos^2(a)+sin^2(a)	prove\:\tan(a)\cot(a)=\cos^{2}(a)+\sin^{2}(a)
prove 1+tan^2(t)= 1/(cos^2(t))	prove\:1+\tan^{2}(t)=\frac{1}{\cos^{2}(t)}
prove (sin^2(θ))/(cos(θ))=tan(θ)sin(θ)	prove\:\frac{\sin^{2}(θ)}{\cos(θ)}=\tan(θ)\sin(θ)
prove cos^2(x)csc(x)sec(x)=cot(x)	prove\:\cos^{2}(x)\csc(x)\sec(x)=\cot(x)
prove (cos^2(-x)csc(x))/(cot(x))=cos(x)	prove\:\frac{\cos^{2}(-x)\csc(x)}{\cot(x)}=\cos(x)
prove 1+sin(2x)=(sin(x)+cos(x))^2	prove\:1+\sin(2x)=(\sin(x)+\cos(x))^{2}
prove sin^2(θ)-cos^2(θ)sin^2(θ)=sin^4(θ)	prove\:\sin^{2}(θ)-\cos^{2}(θ)\sin^{2}(θ)=\sin^{4}(θ)
prove cot(2x)=(csc^2(x)-2)/(2cot(x))	prove\:\cot(2x)=\frac{\csc^{2}(x)-2}{2\cot(x)}
prove (1+csc(θ))(1-csc(θ))=-cot^2(θ)	prove\:(1+\csc(θ))(1-\csc(θ))=-\cot^{2}(θ)
prove cot(u)tan(u)-sin^2(u)=cos^2(u)	prove\:\cot(u)\tan(u)-\sin^{2}(u)=\cos^{2}(u)
prove 1/(cos(θ))=(tan(θ))/(sin(θ))	prove\:\frac{1}{\cos(θ)}=\frac{\tan(θ)}{\sin(θ)}
prove sin(x)*tan(x)=sec(x)-cos(x)	prove\:\sin(x)\cdot\:\tan(x)=\sec(x)-\cos(x)
prove (tan(y)+cot(y))sin(y)cos(y)=1	prove\:(\tan(y)+\cot(y))\sin(y)\cos(y)=1
prove-2cos^2(x)=sin^4(x)-cos^4(x)-1	prove\:-2\cos^{2}(x)=\sin^{4}(x)-\cos^{4}(x)-1
prove sin(x)*cot(x)=cos(x)	prove\:\sin(x)\cdot\:\cot(x)=\cos(x)
prove (csc(θ)-cot(θ))(csc(θ)+cot(θ))=1	prove\:(\csc(θ)-\cot(θ))(\csc(θ)+\cot(θ))=1
prove 1+sin(x)cot(x)=1+cos(x)	prove\:1+\sin(x)\cot(x)=1+\cos(x)
prove csc(x)-sin(x)=(cot(x))(cos(x))	prove\:\csc(x)-\sin(x)=(\cot(x))(\cos(x))
prove (cos(x))/(sin(x)cot(x))=1	prove\:\frac{\cos(x)}{\sin(x)\cot(x)}=1
prove sin^2(θ)cos(θ)sec(θ)=1-cos^2(θ)	prove\:\sin^{2}(θ)\cos(θ)\sec(θ)=1-\cos^{2}(θ)
prove sin(x)=(cos(x))/(cot(x))	prove\:\sin(x)=\frac{\cos(x)}{\cot(x)}
prove tan^2(θ)-tan^2(θ)sin^2(θ)=sin^2(θ)	prove\:\tan^{2}(θ)-\tan^{2}(θ)\sin^{2}(θ)=\sin^{2}(θ)
prove tan(x)+cot(x)=cot(x)sec^2(x)	prove\:\tan(x)+\cot(x)=\cot(x)\sec^{2}(x)
prove (1+sin(z))(1-sin(z))= 1/(sec^2(z))	prove\:(1+\sin(z))(1-\sin(z))=\frac{1}{\sec^{2}(z)}
prove (tan(x))/(sec(x)+1)=csc(x)-cot(x)	prove\:\frac{\tan(x)}{\sec(x)+1}=\csc(x)-\cot(x)
prove cos^2(x)= 1/(sec^2(x))	prove\:\cos^{2}(x)=\frac{1}{\sec^{2}(x)}
prove ((1+tan(θ)))/(1+cot(θ))=tan(θ)	prove\:\frac{(1+\tan(θ))}{1+\cot(θ)}=\tan(θ)
prove 1+(cos^2(x))/(1+sin(x))=sin(x)	prove\:1+\frac{\cos^{2}(x)}{1+\sin(x)}=\sin(x)
prove sec^2(x)(1-csc^2(x))=-csc^2(x)	prove\:\sec^{2}(x)(1-\csc^{2}(x))=-\csc^{2}(x)
prove-sin^2(x)=cos^2(x)-1	prove\:-\sin^{2}(x)=\cos^{2}(x)-1
prove cos(x)+sin(x)(tan(x))=sec(x)	prove\:\cos(x)+\sin(x)(\tan(x))=\sec(x)
prove (sin(A))/(1-cos(A))-cot(A)=csc(A)	prove\:\frac{\sin(A)}{1-\cos(A)}-\cot(A)=\csc(A)
prove (cos(2x)-sin(2x))^2-1=sin(-4x)	prove\:(\cos(2x)-\sin(2x))^{2}-1=\sin(-4x)
prove cot^2(x)+1/(cos(x)sec(x))=csc^2(x)	prove\:\cot^{2}(x)+\frac{1}{\cos(x)\sec(x)}=\csc^{2}(x)
prove (1+cos(θ))/(sin(θ))=csc(θ)+cot(θ)	prove\:\frac{1+\cos(θ)}{\sin(θ)}=\csc(θ)+\cot(θ)
prove (cos(x+y)+cos(x-y))/(sin(x-y)+sin(x+y))=cot(x)	prove\:\frac{\cos(x+y)+\cos(x-y)}{\sin(x-y)+\sin(x+y)}=\cot(x)
prove tan^2(θ)=sec^2(θ)-1	prove\:\tan^{2}(θ)=\sec^{2}(θ)-1
prove (tan(x)+cot(x))^2=csc^2(x)sec^2(x)	prove\:(\tan(x)+\cot(x))^{2}=\csc^{2}(x)\sec^{2}(x)
prove (1+sec(θ))(1-sec(θ))=-tan^2(θ)	prove\:(1+\sec(θ))(1-\sec(θ))=-\tan^{2}(θ)
prove cos(x)=(cot(x))/(csc(x))	prove\:\cos(x)=\frac{\cot(x)}{\csc(x)}
prove tan(θ/2)=(sin(θ))/(1+cos(θ))	prove\:\tan(\frac{θ}{2})=\frac{\sin(θ)}{1+\cos(θ)}
prove cot(t)cos(t)=csc(t)-sin(t)	prove\:\cot(t)\cos(t)=\csc(t)-\sin(t)
prove sin((3pi)/2-x)=-cos(x)	prove\:\sin(\frac{3π}{2}-x)=-\cos(x)
prove sin(x)sec(x)= 1/(cot(x))	prove\:\sin(x)\sec(x)=\frac{1}{\cot(x)}
prove (1-cos(2x))/2 =sin^2(x)	prove\:\frac{1-\cos(2x)}{2}=\sin^{2}(x)
prove (sec(x))/(1-cos(x))=(sec(x)+1)/(sin^2(x))	prove\:\frac{\sec(x)}{1-\cos(x)}=\frac{\sec(x)+1}{\sin^{2}(x)}
prove (1-sin(x))(1+csc(x))=csc(x)-sin(x)	prove\:(1-\sin(x))(1+\csc(x))=\csc(x)-\sin(x)
prove 1-cos^2(θ)=sin^2(θ)	prove\:1-\cos^{2}(θ)=\sin^{2}(θ)
prove tan(pi/4-θ)=(cos(θ)-sin(θ))/(cos(θ)+sin(θ))	prove\:\tan(\frac{π}{4}-θ)=\frac{\cos(θ)-\sin(θ)}{\cos(θ)+\sin(θ)}
prove 2cos^2(x)+sin^2(x)=1+cos^2(x)	prove\:2\cos^{2}(x)+\sin^{2}(x)=1+\cos^{2}(x)
prove csc(B)-sin(B)=cot(B)cos(B)	prove\:\csc(B)-\sin(B)=\cot(B)\cos(B)
prove (1+sec^2(θ))/(sec^2(θ))=1+cos^2(θ)	prove\:\frac{1+\sec^{2}(θ)}{\sec^{2}(θ)}=1+\cos^{2}(θ)
prove cos(2a+a)=-3cos(a)+4cos^3(a)	prove\:\cos(2a+a)=-3\cos(a)+4\cos^{3}(a)
prove cot(2θ)= 1/2 sec(θ)csc(θ)-tan(θ)	prove\:\cot(2θ)=\frac{1}{2}\sec(θ)\csc(θ)-\tan(θ)
prove csc^2(θ)-cos(θ)sec(θ)=cot^2(θ)	prove\:\csc^{2}(θ)-\cos(θ)\sec(θ)=\cot^{2}(θ)
prove sin(x)+cos(x)=1	prove\:\sin(x)+\cos(x)=1
prove 8cos^2(x)-8sin^2(x)=8-16sin^2(x)	prove\:8\cos^{2}(x)-8\sin^{2}(x)=8-16\sin^{2}(x)
prove sec(x)-sin(x)*tan(x)=cos(x)	prove\:\sec(x)-\sin(x)\cdot\:\tan(x)=\cos(x)
prove (sec(x)csc(x))/(cot(x))=sec^2(x)	prove\:\frac{\sec(x)\csc(x)}{\cot(x)}=\sec^{2}(x)
prove (sin(θ)-cos(θ))^2=1-2sin(θ)cos(θ)	prove\:(\sin(θ)-\cos(θ))^{2}=1-2\sin(θ)\cos(θ)
prove cot(θ)sin(θ)sec(θ)=1	prove\:\cot(θ)\sin(θ)\sec(θ)=1
prove cos^4(x)=1-2sin^2(x)+sin^4(x)	prove\:\cos^{4}(x)=1-2\sin^{2}(x)+\sin^{4}(x)
prove tan(x)*cos(x)=sin(x)	prove\:\tan(x)\cdot\:\cos(x)=\sin(x)
prove cos^2(x)csc^2(x)=csc^2(x)-1	prove\:\cos^{2}(x)\csc^{2}(x)=\csc^{2}(x)-1
prove (sin(2θ))/(1+cos(2θ))=tan(θ)	prove\:\frac{\sin(2θ)}{1+\cos(2θ)}=\tan(θ)
prove (sec(x)+tan(x))/(csc(x)+1)=tan(x)	prove\:\frac{\sec(x)+\tan(x)}{\csc(x)+1}=\tan(x)
prove tan(a)=(sec(a))/(csc(a))	prove\:\tan(a)=\frac{\sec(a)}{\csc(a)}
prove sec(x)tan(x)cos(x)cot(x)=1	prove\:\sec(x)\tan(x)\cos(x)\cot(x)=1
prove 1-sec(x)cos^3(x)=sin^2(x)	prove\:1-\sec(x)\cos^{3}(x)=\sin^{2}(x)
prove sin(2x)(1-cos(2x))=4sin^3(x)cos(x)	prove\:\sin(2x)(1-\cos(2x))=4\sin^{3}(x)\cos(x)
prove cot(θ)-2cot(2θ)=tan(θ)	prove\:\cot(θ)-2\cot(2θ)=\tan(θ)
prove tan(3pi+θ)=tan(θ)	prove\:\tan(3π+θ)=\tan(θ)
prove 4sin(-x)cos(-x)=-2sin(2x)	prove\:4\sin(-x)\cos(-x)=-2\sin(2x)
prove (4sin(θ)+4cos(θ))^2=16+16sin(2θ)	prove\:(4\sin(θ)+4\cos(θ))^{2}=16+16\sin(2θ)
prove 1-sin(θ)=cos^2(θ)	prove\:1-\sin(θ)=\cos^{2}(θ)
prove 1/(sec(a)-tan(a))=sec(a)+tan(a)	prove\:\frac{1}{\sec(a)-\tan(a)}=\sec(a)+\tan(a)
prove sin(x)cos(x)=1	prove\:\sin(x)\cos(x)=1
prove sec^2(θ)-sin^2(θ)sec^2(θ)=1	prove\:\sec^{2}(θ)-\sin^{2}(θ)\sec^{2}(θ)=1
prove 9cot^2(y)(sec^2(y)-1)=9	prove\:9\cot^{2}(y)(\sec^{2}(y)-1)=9
prove sin(x)cos(x)= 1/2 sin(2x)	prove\:\sin(x)\cos(x)=\frac{1}{2}\sin(2x)
prove (tan^2(t)-1)/(sec^2(t))=(tan(t)-cot(t))/(tan(t)+cot(t))	prove\:\frac{\tan^{2}(t)-1}{\sec^{2}(t)}=\frac{\tan(t)-\cot(t)}{\tan(t)+\cot(t)}
prove 8sin(x)cos(x)=4sin(2x)	prove\:8\sin(x)\cos(x)=4\sin(2x)
prove tan(x)cos(x)-1/(csc(x))=0	prove\:\tan(x)\cos(x)-\frac{1}{\csc(x)}=0
prove sec(a)-cos(a)=sin(a)tan(a)	prove\:\sec(a)-\cos(a)=\sin(a)\tan(a)
prove (sec(x)+tan(x))(1-sin(x))=cos(x)	prove\:(\sec(x)+\tan(x))(1-\sin(x))=\cos(x)
prove sin^7(x)=(1-cos^2(x))^3sin(x)	prove\:\sin^{7}(x)=(1-\cos^{2}(x))^{3}\sin(x)
prove tan(A)+cot(A)=sec(A)csc(A)	prove\:\tan(A)+\cot(A)=\sec(A)\csc(A)
prove (sec(θ))/(csc(θ))=tan(θ)	prove\:\frac{\sec(θ)}{\csc(θ)}=\tan(θ)
prove cos(2x)+1=2cos^2(x)	prove\:\cos(2x)+1=2\cos^{2}(x)
prove tan(θ)*cos(θ)=sin(θ)	prove\:\tan(θ)\cdot\:\cos(θ)=\sin(θ)
prove csc(x)+cot(x)=(1+cos(x))/(sin(x))	prove\:\csc(x)+\cot(x)=\frac{1+\cos(x)}{\sin(x)}
prove (cos(x))/(1-sin(x))=tan(x/2-pi/4)	prove\:\frac{\cos(x)}{1-\sin(x)}=\tan(\frac{x}{2}-\frac{π}{4})
prove (sin(x))^2=sin^2(x)	prove\:(\sin(x))^{2}=\sin^{2}(x)
prove (cos(x))/(sec(x)-1)-(cos(x))/(sec(x)+1)=(2cos(x))/(tan^2(x))	prove\:\frac{\cos(x)}{\sec(x)-1}-\frac{\cos(x)}{\sec(x)+1}=\frac{2\cos(x)}{\tan^{2}(x)}
prove cot(x-y)=(cot(x)cot(y)+1)/(cot(y)-cot(x))	prove\:\cot(x-y)=\frac{\cot(x)\cot(y)+1}{\cot(y)-\cot(x)}
prove (cot(a))/(cos(a))=csc(a)	prove\:\frac{\cot(a)}{\cos(a)}=\csc(a)
prove cos(2θ)=(2-sec^2(θ))/(sec^2(θ))	prove\:\cos(2θ)=\frac{2-\sec^{2}(θ)}{\sec^{2}(θ)}
prove cos^2(x)tan^2(x)+cos^2(x)=1	prove\:\cos^{2}(x)\tan^{2}(x)+\cos^{2}(x)=1
prove (csc(θ)sin(θ))/(sec(θ))=cos(θ)	prove\:\frac{\csc(θ)\sin(θ)}{\sec(θ)}=\cos(θ)
prove tan(x)cot(x)-sin^2(x)=cos^2(x)	prove\:\tan(x)\cot(x)-\sin^{2}(x)=\cos^{2}(x)

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