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Popular Trigonometry Problems

prove sin(2x)+sin(x)=0	prove\:\sin(2x)+\sin(x)=0
prove (cot(θ))/(csc(θ))=cot(θ)csc(θ)	prove\:\frac{\cot(θ)}{\csc(θ)}=\cot(θ)\csc(θ)
prove 1=cos(x)csc(x)tan(x)	prove\:1=\cos(x)\csc(x)\tan(x)
prove csc^2(x)+sec^2(x)=1	prove\:\csc^{2}(x)+\sec^{2}(x)=1
prove 3-3cos^2(x)+4-4sin^2(x)=3+cos^2(x)	prove\:3-3\cos^{2}(x)+4-4\sin^{2}(x)=3+\cos^{2}(x)
prove-(1+cot^2(x))=-csc^2(x)	prove\:-(1+\cot^{2}(x))=-\csc^{2}(x)
prove (sin(a)+tan(a))/(1+cos(a))=tan(a)	prove\:\frac{\sin(a)+\tan(a)}{1+\cos(a)}=\tan(a)
prove (4sec(x)-4)/(1-cos(θ))=4sec(x)	prove\:\frac{4\sec(x)-4}{1-\cos(θ)}=4\sec(x)
prove 1+cot^2(x)=(tan^2(x)+1)/(tan^2(x))	prove\:1+\cot^{2}(x)=\frac{\tan^{2}(x)+1}{\tan^{2}(x)}
prove sin(180+θ)=-sin(θ)	prove\:\sin(180^{\circ\:}+θ)=-\sin(θ)
prove (1-tan^2(x))/(1+tan^2(x))=sec(x)	prove\:\frac{1-\tan^{2}(x)}{1+\tan^{2}(x)}=\sec(x)
prove 2sec(x)=2+2tan(x)	prove\:2\sec(x)=2+2\tan(x)
prove sin^2(θ)(1+cos^2(θ))=1	prove\:\sin^{2}(θ)(1+\cos^{2}(θ))=1
prove sin(x)tan(x)=cos(x)	prove\:\sin(x)\tan(x)=\cos(x)
prove 2sin^2(x/2)+4cos^2(x/2)-3=cos(x)	prove\:2\sin^{2}(\frac{x}{2})+4\cos^{2}(\frac{x}{2})-3=\cos(x)
prove tan(2u)=((2tan(u)))/(1-tan^2(u))	prove\:\tan(2u)=\frac{(2\tan(u))}{1-\tan^{2}(u)}
prove 1/(-sin(x))=sec(x)tan(x)	prove\:\frac{1}{-\sin(x)}=\sec(x)\tan(x)
prove 6cos(θ)=6cos(-θ)	prove\:6\cos(θ)=6\cos(-θ)
prove ((tan(2x)+cot(2x)))/(csc(2x))=sec(2x)	prove\:\frac{(\tan(2x)+\cot(2x))}{\csc(2x)}=\sec(2x)
prove (cos(θ)-sin(θ))^2=1	prove\:(\cos(θ)-\sin(θ))^{2}=1
prove cos(x)=1=cos(0)=1	prove\:\cos(x)=1=\cos(0)=1
prove (tan(x)+1)(tan(x)-1)=sec^2(x)-2	prove\:(\tan(x)+1)(\tan(x)-1)=\sec^{2}(x)-2
prove 1/(csc(x)+1)= 1/(sin(x)+1)	prove\:\frac{1}{\csc(x)+1}=\frac{1}{\sin(x)+1}
prove tan(θ)+1=(sin(θ))/(cos(θ))+1	prove\:\tan(θ)+1=\frac{\sin(θ)}{\cos(θ)}+1
prove (1+tan^2(α))cos^2(α)=1	prove\:(1+\tan^{2}(α))\cos^{2}(α)=1
prove 1/(sin^2(x))= 1/(csc^2(x))	prove\:\frac{1}{\sin^{2}(x)}=\frac{1}{\csc^{2}(x)}
prove sin(x)(1+tan^2(x))=sin(x)sec^2(x)	prove\:\sin(x)(1+\tan^{2}(x))=\sin(x)\sec^{2}(x)
prove (tan^2(X))/(1+cot^2(X))=sin^4(X)	prove\:\frac{\tan^{2}(X)}{1+\cot^{2}(X)}=\sin^{4}(X)
prove sin(x)+cot(x)cos(x)= 1/(sin(x))	prove\:\sin(x)+\cot(x)\cos(x)=\frac{1}{\sin(x)}
prove 1+cos(6x)=2cos^2(3x)	prove\:1+\cos(6x)=2\cos^{2}(3x)
prove (sec(a))/(cot(a)+tan(a))=sin(a)	prove\:\frac{\sec(a)}{\cot(a)+\tan(a)}=\sin(a)
prove (4+2sin(θ))/(1-sin(θ))=3	prove\:\frac{4+2\sin(θ)}{1-\sin(θ)}=3
prove (sin(4x))/4 =4(sin(x)cos(x))/4	prove\:\frac{\sin(4x)}{4}=4\frac{\sin(x)\cos(x)}{4}
prove (sin^2(x))/(1-sin^2(x))=tan^2(x)	prove\:\frac{\sin^{2}(x)}{1-\sin^{2}(x)}=\tan^{2}(x)
prove sin(-30)=-sin(30)	prove\:\sin(-30^{\circ\:})=-\sin(30^{\circ\:})
prove cos(1/2 pi-x)=sin(x)	prove\:\cos(\frac{1}{2}π-x)=\sin(x)
prove sin(x)-cos(x)+1=cos(x)	prove\:\sin(x)-\cos(x)+1=\cos(x)
prove cos(12x)=1-2sin^2(6x)	prove\:\cos(12x)=1-2\sin^{2}(6x)
prove tan(θ)=tan(pi+θ)	prove\:\tan(θ)=\tan(π+θ)
prove cos(x)-cos^3(x)=cos(x)-sin^2(x)	prove\:\cos(x)-\cos^{3}(x)=\cos(x)-\sin^{2}(x)
prove cos(B)csc(B)tan(B)=11	prove\:\cos(B)\csc(B)\tan(B)=11
prove tan(8x)=(8tan(x))/(1-tan^2(x))	prove\:\tan(8x)=\frac{8\tan(x)}{1-\tan^{2}(x)}
prove tan(-a)=(cos(pi/2+a))/(cos(a))	prove\:\tan(-a)=\frac{\cos(\frac{π}{2}+a)}{\cos(a)}
prove sin(θ)-1/(sin(θ))=cos(θ)	prove\:\sin(θ)-\frac{1}{\sin(θ)}=\cos(θ)
prove cos^8(x)=sin^7(x)cos^1(x)	prove\:\cos^{8}(x)=\sin^{7}(x)\cos^{1}(x)
prove (cot(x)+1)^2-2cot(x)=csc^2(x)	prove\:(\cot(x)+1)^{2}-2\cot(x)=\csc^{2}(x)
prove cos(θ)= 1/3	prove\:\cos(θ)=\frac{1}{3}
prove sec(θ)-(tan(θ))/(csc(θ))=cos(θ)	prove\:\sec(θ)-\frac{\tan(θ)}{\csc(θ)}=\cos(θ)
prove sec^2(x)=(1+tan^2(x))	prove\:\sec^{2}(x)=(1+\tan^{2}(x))
prove cot^2(x)sec^2(x)=cot^2(x)+1	prove\:\cot^{2}(x)\sec^{2}(x)=\cot^{2}(x)+1
prove (sin(x))/(cos(x)+sin(x))=1	prove\:\frac{\sin(x)}{\cos(x)+\sin(x)}=1
prove cos(x)=(cot(x))/(tan(x))	prove\:\cos(x)=\frac{\cot(x)}{\tan(x)}
prove cos^2(2a)-sin^2(2a)=cos(4a)	prove\:\cos^{2}(2a)-\sin^{2}(2a)=\cos(4a)
prove tan(2x)-2cos(x)=0	prove\:\tan(2x)-2\cos(x)=0
prove cos^2(a)cot^2(a)=cot^2(a)-cos^2(a)	prove\:\cos^{2}(a)\cot^{2}(a)=\cot^{2}(a)-\cos^{2}(a)
prove cos(θ)= 1/2	prove\:\cos(θ)=\frac{1}{2}
prove csc(2x)= 1/(sin^2(x)-1)	prove\:\csc(2x)=\frac{1}{\sin^{2}(x)-1}
prove (1+tan^2(α))(1-sin^2(α))=1	prove\:(1+\tan^{2}(α))(1-\sin^{2}(α))=1
prove csc(θ)-cot(θ)=(1-cos(θ))/(sin(θ))	prove\:\csc(θ)-\cot(θ)=\frac{1-\cos(θ)}{\sin(θ)}
prove tan(x)=tan(x)+2sin^2(x)	prove\:\tan(x)=\tan(x)+2\sin^{2}(x)
prove 1/(2cot(1-cos^2(x)))=csc(2x)	prove\:\frac{1}{2\cot(1-\cos^{2}(x))}=\csc(2x)
prove cot(u)= 1/(tan(u))	prove\:\cot(u)=\frac{1}{\tan(u)}
prove-sin(2x)=-4cos(x)sin(x)	prove\:-\sin(2x)=-4\cos(x)\sin(x)
prove cos(θ)(tan(θ)-sec(-θ))=sin(θ)-1	prove\:\cos(θ)(\tan(θ)-\sec(-θ))=\sin(θ)-1
prove cos(pi/2)=-0	prove\:\cos(\frac{π}{2})=-0
prove cos(x)+1=sin(2x)	prove\:\cos(x)+1=\sin(2x)
prove ((sec^2(x)))/(sec^2(x)-1)=csc^2(x)	prove\:\frac{(\sec^{2}(x))}{\sec^{2}(x)-1}=\csc^{2}(x)
prove (sin(x))(tan(x)cos(x)-cot(x)cos(x))=1-2cos(2x)	prove\:(\sin(x))(\tan(x)\cos(x)-\cot(x)\cos(x))=1-2\cos(2x)
prove sin(20)=2cos(10)*sin(10)	prove\:\sin(20^{\circ\:})=2\cos(10^{\circ\:})\cdot\:\sin(10^{\circ\:})
prove sin^2(x)=sec(x)cos(x)-cos^2(x)	prove\:\sin^{2}(x)=\sec(x)\cos(x)-\cos^{2}(x)
prove 1-2sin^2(2θ)=8cos^4(θ)-8cos^2(θ)+1	prove\:1-2\sin^{2}(2θ)=8\cos^{4}(θ)-8\cos^{2}(θ)+1
prove sech^2(x)+tanh^2(x)=1	prove\:\sech^{2}(x)+\tanh^{2}(x)=1
prove 2cos^2(A)-cos(2A)-1=0	prove\:2\cos^{2}(A)-\cos(2A)-1=0
prove (cot(x)+1)/(cos(x)+sin(x))=csc(x)	prove\:\frac{\cot(x)+1}{\cos(x)+\sin(x)}=\csc(x)
prove csc(A)= 7/4	prove\:\csc(A)=\frac{7}{4}
prove (sin^2(x))/(sin^2(x))=sin(x)	prove\:\frac{\sin^{2}(x)}{\sin^{2}(x)}=\sin(x)
prove csc(cos(+sin(x)))=cot(+1)	prove\:\csc(\cos(+\sin(x)))=\cot(+1)
prove 4sin(x/2)cos(x/2)=2sin(x)	prove\:4\sin(\frac{x}{2})\cos(\frac{x}{2})=2\sin(x)
prove 5cos(x)-3=3cos(x)-4	prove\:5\cos(x)-3=3\cos(x)-4
prove (cos(φ)+1)/(sin(φ)+tan(φ))=cot(φ)	prove\:\frac{\cos(φ)+1}{\sin(φ)+\tan(φ)}=\cot(φ)
prove tan(x)+tan(x)=0	prove\:\tan(x)+\tan(x)=0
prove 2cos^2(x)-cos(2x)=1	prove\:2\cos^{2}(x)-\cos(2x)=1
prove-cot^2(x)=1-csc^2(x)	prove\:-\cot^{2}(x)=1-\csc^{2}(x)
prove 1/(tan(2θ))=(cot^2(θ)-1)/(2cot(θ))	prove\:\frac{1}{\tan(2θ)}=\frac{\cot^{2}(θ)-1}{2\cot(θ)}
prove (1-cos(θ))+sin^2(θ)=2	prove\:(1-\cos(θ))+\sin^{2}(θ)=2
prove 1/(sec(θ))=(sec(θ))^{-1}	prove\:\frac{1}{\sec(θ)}=(\sec(θ))^{-1}
prove sin(2θ)+cos(2θ)=1	prove\:\sin(2θ)+\cos(2θ)=1
prove 25(sec^2(5x)-tan^2(5x))=25	prove\:25(\sec^{2}(5x)-\tan^{2}(5x))=25
prove cot^2(x)=((cos^2(x)))/(1-cos^2(x))	prove\:\cot^{2}(x)=\frac{(\cos^{2}(x))}{1-\cos^{2}(x)}
prove+(cos(x))/(1-sin(x))=sec(x)+tan(x)	prove\:+\frac{\cos(x)}{1-\sin(x)}=\sec(x)+\tan(x)
prove sin((4pi)/3)=sqrt(3)cos((2pi)/3)	prove\:\sin(\frac{4π}{3})=\sqrt{3}\cos(\frac{2π}{3})
prove sin^2(x)+sin^2(θ)=1	prove\:\sin^{2}(x)+\sin^{2}(θ)=1
prove (cot(x)-sec(x))/(csc(x))=1	prove\:\frac{\cot(x)-\sec(x)}{\csc(x)}=1
prove 1+tan^2(x)+cot(x)=sec^2(x)+cos(x)	prove\:1+\tan^{2}(x)+\cot(x)=\sec^{2}(x)+\cos(x)
prove cos(θ)sec(θ)=tan(θ)cot(θ)	prove\:\cos(θ)\sec(θ)=\tan(θ)\cot(θ)
prove cos(x)-cos(x)=2cos(x)	prove\:\cos(x)-\cos(x)=2\cos(x)
prove (cos^2(2θ))/2 =(1+cos(4θ))/8	prove\:\frac{\cos^{2}(2θ)}{2}=\frac{1+\cos(4θ)}{8}
prove (cos^2(x))/(sin^2(x))+1=csc^2(x)	prove\:\frac{\cos^{2}(x)}{\sin^{2}(x)}+1=\csc^{2}(x)
prove cot(x)-cot(x)cos^2(x)=sin(x)cos(x)	prove\:\cot(x)-\cot(x)\cos^{2}(x)=\sin(x)\cos(x)
prove 1/(sec(θ))=arcsec(θ)	prove\:\frac{1}{\sec(θ)}=\arcsec(θ)

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