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Popular Trigonometry Problems

prove sin^2(θ)+2cos^2(θ)-1=cos^2(θ)	prove\:\sin^{2}(θ)+2\cos^{2}(θ)-1=\cos^{2}(θ)
prove 1/(sin(x)cos(x))=2csc(2x)	prove\:\frac{1}{\sin(x)\cos(x)}=2\csc(2x)
prove (cos(x)+sin(x))^2=2sin(x)cos(x)+1	prove\:(\cos(x)+\sin(x))^{2}=2\sin(x)\cos(x)+1
prove cos(θ)=-cos(-θ)	prove\:\cos(θ)=-\cos(-θ)
prove sin(θ)+cos(θ)=sin(θ+45)	prove\:\sin(θ)+\cos(θ)=\sin(θ+45^{\circ\:})
prove cot(t)-sin(2t)=cot(t)cos(2t)	prove\:\cot(t)-\sin(2t)=\cot(t)\cos(2t)
prove (sin(2θ))/(sin(θ))=2cos(θ)	prove\:\frac{\sin(2θ)}{\sin(θ)}=2\cos(θ)
prove sqrt(81-9(3sin(x))^2)=1	prove\:\sqrt{81-9(3\sin(x))^{2}}=1
prove (1+sec(x))/(csc(x))=sin(x)+tan(x)	prove\:\frac{1+\sec(x)}{\csc(x)}=\sin(x)+\tan(x)
prove (tan^2(t))/(sec(t))=sec(t)-cot(t)	prove\:\frac{\tan^{2}(t)}{\sec(t)}=\sec(t)-\cot(t)
prove sqrt(81-9(3sin(x))^2)=9cos(x)	prove\:\sqrt{81-9(3\sin(x))^{2}}=9\cos(x)
prove 25tan^2(5x)+25=25+(5tan(5x))^2	prove\:25\tan^{2}(5x)+25=25+(5\tan(5x))^{2}
prove (1+tan(a))*(1-tan(a))=2-sec^2(a)	prove\:(1+\tan(a))\cdot\:(1-\tan(a))=2-\sec^{2}(a)
prove (cot(x))(sec(x))(sin(x))=1	prove\:(\cot(x))(\sec(x))(\sin(x))=1
prove (cos^2(x)-4)/(cos(x)-2)=cos(x)+2	prove\:\frac{\cos^{2}(x)-4}{\cos(x)-2}=\cos(x)+2
prove sin^2(a)tan^2(a)=tan^2(a)-sin^2(a)	prove\:\sin^{2}(a)\tan^{2}(a)=\tan^{2}(a)-\sin^{2}(a)
prove (cos(a))/(1-sin(a))-tan(a)=sec(a)	prove\:\frac{\cos(a)}{1-\sin(a)}-\tan(a)=\sec(a)
prove 1/(1+cos(θ))=csc^2(θ)-csc(θ)cot(θ)	prove\:\frac{1}{1+\cos(θ)}=\csc^{2}(θ)-\csc(θ)\cot(θ)
prove tan(θ)(sin(θ)+cot(θ)cos(θ))=sec(θ)	prove\:\tan(θ)(\sin(θ)+\cot(θ)\cos(θ))=\sec(θ)
prove sin(x+y)=sin(x)+sin(y)	prove\:\sin(x+y)=\sin(x)+\sin(y)
prove tan(θ/2)+cot(θ/2)=2csc(θ)	prove\:\tan(\frac{θ}{2})+\cot(\frac{θ}{2})=2\csc(θ)
prove sin^2(2θ)=4sin^2(θ)cos^2(θ)	prove\:\sin^{2}(2θ)=4\sin^{2}(θ)\cos^{2}(θ)
prove csc(t)+cot(t)=(tan(t))/(sec(t)-1)	prove\:\csc(t)+\cot(t)=\frac{\tan(t)}{\sec(t)-1}
prove (cos(4x)+cos(6x))/(sin(4x)-sin(6x))=-cot(x)	prove\:\frac{\cos(4x)+\cos(6x)}{\sin(4x)-\sin(6x)}=-\cot(x)
prove 2sin^2(x)=(1-cos(2x))	prove\:2\sin^{2}(x)=(1-\cos(2x))
prove (sec^2(x))(1-cos^2(x))=tan^2(x)	prove\:(\sec^{2}(x))(1-\cos^{2}(x))=\tan^{2}(x)
prove 2sin(4x)=4sin(2x)cos(2x)	prove\:2\sin(4x)=4\sin(2x)\cos(2x)
prove cos^2(x)(1-tan^2(x))=cos(2x)	prove\:\cos^{2}(x)(1-\tan^{2}(x))=\cos(2x)
prove 1/(cos^2(x))=(1/(cos(x)))^2	prove\:\frac{1}{\cos^{2}(x)}=(\frac{1}{\cos(x)})^{2}
prove (tan(x))/(1+tan^2(x))=sin(x)cos(x)	prove\:\frac{\tan(x)}{1+\tan^{2}(x)}=\sin(x)\cos(x)
prove cos^3(2x)=(1-sin^2(2x))cos(2x)	prove\:\cos^{3}(2x)=(1-\sin^{2}(2x))\cos(2x)
prove 1-((cos^2(θ)))/(1+sin(θ))=sin(θ)	prove\:1-\frac{(\cos^{2}(θ))}{1+\sin(θ)}=\sin(θ)
prove tan(180-y)=-tan(y)	prove\:\tan(180^{\circ\:}-y)=-\tan(y)
prove cot(2x)=(cot(2x)-1)/(2cot(x))	prove\:\cot(2x)=\frac{\cot(2x)-1}{2\cot(x)}
prove tan^2(x)csc^2(x)-tan^2(x)=1	prove\:\tan^{2}(x)\csc^{2}(x)-\tan^{2}(x)=1
prove 1/(csc^2(x))=1-cos^2(x)	prove\:\frac{1}{\csc^{2}(x)}=1-\cos^{2}(x)
prove tan^2(x)-(sec(x)+1)(sec(x)-1)=0	prove\:\tan^{2}(x)-(\sec(x)+1)(\sec(x)-1)=0
prove csc(u)sin(u)-cos^2(u)=sin^2(u)	prove\:\csc(u)\sin(u)-\cos^{2}(u)=\sin^{2}(u)
prove 2cos^2(u)-cos(2u)=1	prove\:2\cos^{2}(u)-\cos(2u)=1
prove sec^4(θ)=sec^2(θ)tan^2(θ)+sec^2(θ)	prove\:\sec^{4}(θ)=\sec^{2}(θ)\tan^{2}(θ)+\sec^{2}(θ)
prove sin^2(θ)=1-1/(sec^2(θ))	prove\:\sin^{2}(θ)=1-\frac{1}{\sec^{2}(θ)}
prove tan(θ)sec(θ)csc(θ)=1+tan^2(θ)	prove\:\tan(θ)\sec(θ)\csc(θ)=1+\tan^{2}(θ)
prove (cos(t))/(1-sin(t))-tan(t)=sec(t)	prove\:\frac{\cos(t)}{1-\sin(t)}-\tan(t)=\sec(t)
prove (1-cos(x))/(1/(cos(x))-1)=cos(x)	prove\:\frac{1-\cos(x)}{\frac{1}{\cos(x)}-1}=\cos(x)
prove sin(pi-0)=sin(0)	prove\:\sin(π-0)=\sin(0)
prove cos^2(0/2)=sec(0)	prove\:\cos^{2}(\frac{0}{2})=\sec(0)
prove csc^2(x)+1=cot^2(x)+2	prove\:\csc^{2}(x)+1=\cot^{2}(x)+2
prove sin^2(a)=1-cos^2(a)	prove\:\sin^{2}(a)=1-\cos^{2}(a)
prove (2sin(x)-2cos(x))^2=-4sin(2x)+4	prove\:(2\sin(x)-2\cos(x))^{2}=-4\sin(2x)+4
prove (sin(x))/(cot^2(x))=(tan^2(x))/(csc(x))	prove\:\frac{\sin(x)}{\cot^{2}(x)}=\frac{\tan^{2}(x)}{\csc(x)}
prove sin(x)*(1+cot(x))=sin(x)+cos(x)	prove\:\sin(x)\cdot\:(1+\cot(x))=\sin(x)+\cos(x)
prove sin((5pi)/4)=cos((5pi)/4)	prove\:\sin(\frac{5π}{4})=\cos(\frac{5π}{4})
prove 2sin^2(x)-cos^2(x)(tan^2(x)-1)=1	prove\:2\sin^{2}(x)-\cos^{2}(x)(\tan^{2}(x)-1)=1
prove cot(a)-1=(csc(a)-sec(a))/(sec(a))	prove\:\cot(a)-1=\frac{\csc(a)-\sec(a)}{\sec(a)}
prove tan(135+θ)=(-1+tan(θ))/(1+tan(θ))	prove\:\tan(135^{\circ\:}+θ)=\frac{-1+\tan(θ)}{1+\tan(θ)}
prove (csc(pi/2-x))/(-tan(-x))=csc(x)	prove\:\frac{\csc(\frac{π}{2}-x)}{-\tan(-x)}=\csc(x)
prove cot^2(θ)cos^2(θ)=cot^2(θ)-cos^2(θ)	prove\:\cot^{2}(θ)\cos^{2}(θ)=\cot^{2}(θ)-\cos^{2}(θ)
prove tan(120)=tan(180-60)	prove\:\tan(120^{\circ\:})=\tan(180^{\circ\:}-60^{\circ\:})
prove sin(2x)tan(x)=2sin^2(x)	prove\:\sin(2x)\tan(x)=2\sin^{2}(x)
prove cot(b)sec(b)sin(b)=1	prove\:\cot(b)\sec(b)\sin(b)=1
prove ((sec^2(Q)-1))/(sec^2(Q))=sin^2(Q)	prove\:\frac{(\sec^{2}(Q)-1)}{\sec^{2}(Q)}=\sin^{2}(Q)
prove 1-tan^2(A)cos^2(A)=cos^2(A)	prove\:1-\tan^{2}(A)\cos^{2}(A)=\cos^{2}(A)
prove 1/(1-tan(θ))-1/(1+tan(θ))=tan(2θ)	prove\:\frac{1}{1-\tan(θ)}-\frac{1}{1+\tan(θ)}=\tan(2θ)
prove tan(x)+cot(x)= 1/(sin(x)*cos(x))	prove\:\tan(x)+\cot(x)=\frac{1}{\sin(x)\cdot\:\cos(x)}
prove (1-4sec^2(x))/(1+2sec(x))=1-2sec(x)	prove\:\frac{1-4\sec^{2}(x)}{1+2\sec(x)}=1-2\sec(x)
prove sin((3pi)/4)=(sqrt(2))/2	prove\:\sin(\frac{3π}{4})=\frac{\sqrt{2}}{2}
prove tan(x)=cot(pi/2-x)	prove\:\tan(x)=\cot(\frac{π}{2}-x)
prove (tan(x)+1)/(sec(x)+csc(x))=sin(x)	prove\:\frac{\tan(x)+1}{\sec(x)+\csc(x)}=\sin(x)
prove sec(2x)=(csc^2(x))/(csc^2(x)-2)	prove\:\sec(2x)=\frac{\csc^{2}(x)}{\csc^{2}(x)-2}
prove 4-3sin^2(2x)=4(sin^6(x)+cos^6(x))	prove\:4-3\sin^{2}(2x)=4(\sin^{6}(x)+\cos^{6}(x))
prove (1-cos(a))/(1+cos(a))=tan^2(a/2)	prove\:\frac{1-\cos(a)}{1+\cos(a)}=\tan^{2}(\frac{a}{2})
prove 1+(cot^2(θ))/(csc(θ)+1)=csc(θ)	prove\:1+\frac{\cot^{2}(θ)}{\csc(θ)+1}=\csc(θ)
prove csc^2(x)-cos(x)sec(x)=cot^2(x)	prove\:\csc^{2}(x)-\cos(x)\sec(x)=\cot^{2}(x)
prove (sin^2(a))/(1-sin^2(a))=sec^2(a)-1	prove\:\frac{\sin^{2}(a)}{1-\sin^{2}(a)}=\sec^{2}(a)-1
prove (1-cos^2(x))/(1+cos(x))=1-cos(x)	prove\:\frac{1-\cos^{2}(x)}{1+\cos(x)}=1-\cos(x)
prove (1-sin^2(x))/(1-cos^2(x))=cot^2(x)	prove\:\frac{1-\sin^{2}(x)}{1-\cos^{2}(x)}=\cot^{2}(x)
prove tan^2(x/2)=(1-cos(x))/(1+cos(x))	prove\:\tan^{2}(\frac{x}{2})=\frac{1-\cos(x)}{1+\cos(x)}
prove sin(2θ)+2sin(θ)-cos(θ)=2	prove\:\sin(2θ)+2\sin(θ)-\cos(θ)=2
prove csc(x)-cos^2(x)=sin(x)	prove\:\csc(x)-\cos^{2}(x)=\sin(x)
prove (csc(x)+1)/(cot(x)+cos(x))=sec(x)	prove\:\frac{\csc(x)+1}{\cot(x)+\cos(x)}=\sec(x)
prove (sin(-x)cot(x))/(sin(pi/2-x))=1	prove\:\frac{\sin(-x)\cot(x)}{\sin(\frac{π}{2}-x)}=1
prove csc^2(θ/2)= 2/(1-cos(θ))	prove\:\csc^{2}(\frac{θ}{2})=\frac{2}{1-\cos(θ)}
prove sec(x)cos(x)+tan^2(x)=sec^2(x)	prove\:\sec(x)\cos(x)+\tan^{2}(x)=\sec^{2}(x)
prove (tan^2(θ)+1)/(sec(θ))=sec(θ)	prove\:\frac{\tan^{2}(θ)+1}{\sec(θ)}=\sec(θ)
prove cot^2(θ)+1= 1/(sin^2(θ))	prove\:\cot^{2}(θ)+1=\frac{1}{\sin^{2}(θ)}
prove 3cos(2x+pi/2)-2=6cos^2(x+pi/4)	prove\:3\cos(2x+\frac{π}{2})-2=6\cos^{2}(x+\frac{π}{4})
prove (sin(x))/(cos(x)cot(x^2))=tan(x)	prove\:\frac{\sin(x)}{\cos(x)\cot(x^{2})}=\tan(x)
prove cot^4(x)=(cos^4(x))/(sin^4(x))	prove\:\cot^{4}(x)=\frac{\cos^{4}(x)}{\sin^{4}(x)}
prove 1/(1-sin(x))+1/(1+sin(x))=2sec(x)	prove\:\frac{1}{1-\sin(x)}+\frac{1}{1+\sin(x)}=2\sec(x)
prove cos^4(b)-sin^4(b)=cos(2b)	prove\:\cos^{4}(b)-\sin^{4}(b)=\cos(2b)
prove tan(x)+cot(x)= 1/(cos(x)sin(x))	prove\:\tan(x)+\cot(x)=\frac{1}{\cos(x)\sin(x)}
prove sin^2(x)sec^2(x)=sec^2(x)-1	prove\:\sin^{2}(x)\sec^{2}(x)=\sec^{2}(x)-1
prove sin^2(x)(1+cot^2(x))-1=0	prove\:\sin^{2}(x)(1+\cot^{2}(x))-1=0
prove (6cos^2(x)-6sin^2(x))=6-12sin^2(x)	prove\:(6\cos^{2}(x)-6\sin^{2}(x))=6-12\sin^{2}(x)
prove (1+cos(x)+cos(2x))/(sin(x)+sin(2x))=cot(x)	prove\:\frac{1+\cos(x)+\cos(2x)}{\sin(x)+\sin(2x)}=\cot(x)
prove 1+1/(tan^2(x))=csc^2(x)	prove\:1+\frac{1}{\tan^{2}(x)}=\csc^{2}(x)
prove cos^2(x)-4=4-sin^2(x)	prove\:\cos^{2}(x)-4=4-\sin^{2}(x)
prove sec(x*0)=1	prove\:\sec(x\cdot\:0)=1
prove (cos(2x))/(sin^2(x))=csc^2(x)-2	prove\:\frac{\cos(2x)}{\sin^{2}(x)}=\csc^{2}(x)-2
prove (2cos(x))/(csc(x)-2sin(x))=tan(2x)	prove\:\frac{2\cos(x)}{\csc(x)-2\sin(x)}=\tan(2x)

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