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Popular Trigonometry Problems

prove tan^2((5pi)/4)=tan((5pi)/4)	prove\:\tan^{2}(\frac{5π}{4})=\tan(\frac{5π}{4})
prove sin(pi/2-θ)=sin(θ-pi/2)	prove\:\sin(\frac{π}{2}-θ)=\sin(θ-\frac{π}{2})
prove (sin^2(x))/((1-cos(x)))=1+cos(x)	prove\:\frac{\sin^{2}(x)}{(1-\cos(x))}=1+\cos(x)
prove cos(-2x)=cos(2x)	prove\:\cos(-2x)=\cos(2x)
prove csc(x)sec(x)= 1/(sin(x)cos(x))	prove\:\csc(x)\sec(x)=\frac{1}{\sin(x)\cos(x)}
prove 1/(csc(θ))=sin(θ)	prove\:\frac{1}{\csc(θ)}=\sin(θ)
prove (1+cos(x))/(1+sec(x))=cos(x)	prove\:\frac{1+\cos(x)}{1+\sec(x)}=\cos(x)
prove 2/(1-cos(θ))=csc^2(θ/2)	prove\:\frac{2}{1-\cos(θ)}=\csc^{2}(\frac{θ}{2})
prove tan^2(x)=(sin(2x))/(1+cos(2x))	prove\:\tan^{2}(x)=\frac{\sin(2x)}{1+\cos(2x)}
prove csc(x)-cot(x)cos(x)= 1/(csc(x))	prove\:\csc(x)-\cot(x)\cos(x)=\frac{1}{\csc(x)}
prove (sin(x))/(1-cos^2(x))=csc(x)	prove\:\frac{\sin(x)}{1-\cos^{2}(x)}=\csc(x)
prove csc(Θ)+sin(-Θ)=(cos^2(Θ))/(sin(Θ))	prove\:\csc(Θ)+\sin(-Θ)=\frac{\cos^{2}(Θ)}{\sin(Θ)}
prove cos(4x)=cos^2(2x)+sin^2(2x)	prove\:\cos(4x)=\cos^{2}(2x)+\sin^{2}(2x)
prove 2sin(x/2)cos(x/2)=sin(x)	prove\:2\sin(\frac{x}{2})\cos(\frac{x}{2})=\sin(x)
prove csc(A)=(cos(2A))/(sin(A))+(sin(2A))/(cos(A))	prove\:\csc(A)=\frac{\cos(2A)}{\sin(A)}+\frac{\sin(2A)}{\cos(A)}
prove sin(θ)csc(θ)+cot(θ)sin(θ)=1+cos(θ)	prove\:\sin(θ)\csc(θ)+\cot(θ)\sin(θ)=1+\cos(θ)
prove tan(x)cot(x)=csc(x)sec(x)	prove\:\tan(x)\cot(x)=\csc(x)\sec(x)
prove sin^2(θ)=1+cos^2(θ)	prove\:\sin^{2}(θ)=1+\cos^{2}(θ)
prove csc(θ)+cos^2(θ)=csc(θ)	prove\:\csc(θ)+\cos^{2}(θ)=\csc(θ)
prove sin(pi/2)=(sqrt(4))/2	prove\:\sin(\frac{π}{2})=\frac{\sqrt{4}}{2}
prove sec(pi/4+a)sec(pi/4-a)=2sec(2a)	prove\:\sec(\frac{π}{4}+a)\sec(\frac{π}{4}-a)=2\sec(2a)
prove sin^4(x)=sec^2(x)tan^2(x)+sec^2(x)	prove\:\sin^{4}(x)=\sec^{2}(x)\tan^{2}(x)+\sec^{2}(x)
prove (1+cos(x))(1-sec(x))=-1	prove\:(1+\cos(x))(1-\sec(x))=-1
prove cot^2(v/2)=((sec(v)+1))/((sec(v)-1))	prove\:\cot^{2}(\frac{v}{2})=\frac{(\sec(v)+1)}{(\sec(v)-1)}
prove csc(θ)(1-cos(θ))(1+cos(θ))=sin(θ)	prove\:\csc(θ)(1-\cos(θ))(1+\cos(θ))=\sin(θ)
prove sec(θ)-1/(sec(θ))=sin(θ)tan(θ)	prove\:\sec(θ)-\frac{1}{\sec(θ)}=\sin(θ)\tan(θ)
prove csc^2(θ)+sec^2(θ)=csc^2(θ)sec^2(θ)	prove\:\csc^{2}(θ)+\sec^{2}(θ)=\csc^{2}(θ)\sec^{2}(θ)
prove sin^2(x)=tan(x)cot(x)-cos^2(x)	prove\:\sin^{2}(x)=\tan(x)\cot(x)-\cos^{2}(x)
prove sin^2(x)-cos^2(x)=1	prove\:\sin^{2}(x)-\cos^{2}(x)=1
prove cot^4(x)+2cot^2(x)=csc^4(x)-1	prove\:\cot^{4}(x)+2\cot^{2}(x)=\csc^{4}(x)-1
prove (sin(2x))/2 = 1/2 sin(2x)	prove\:\frac{\sin(2x)}{2}=\frac{1}{2}\sin(2x)
prove cot(3)=(cos(3))/(sin(3))	prove\:\cot(3)=\frac{\cos(3)}{\sin(3)}
prove (2-2sin^2(x))/(sin(x))=cot(x)	prove\:\frac{2-2\sin^{2}(x)}{\sin(x)}=\cot(x)
prove cos(2θ)-cos(θ)+1=0	prove\:\cos(2θ)-\cos(θ)+1=0
prove (1/(sin(x)+1))+(1/(csc(x)+1))=1	prove\:(\frac{1}{\sin(x)+1})+(\frac{1}{\csc(x)+1})=1
prove (-sin(-a))/(cos(-a))=tan(a)	prove\:\frac{-\sin(-a)}{\cos(-a)}=\tan(a)
prove (tan^2(θ))/(1-cos^2(θ))=sec^2(θ)	prove\:\frac{\tan^{2}(θ)}{1-\cos^{2}(θ)}=\sec^{2}(θ)
prove cos(o)= 1/(sec(o))	prove\:\cos(o)=\frac{1}{\sec(o)}
prove sin(x)=(sec(x))/(tan(x)+cot(x))	prove\:\sin(x)=\frac{\sec(x)}{\tan(x)+\cot(x)}
prove (cot(x)+1)^2=csc^2(x)+2cot(x)	prove\:(\cot(x)+1)^{2}=\csc^{2}(x)+2\cot(x)
prove sin(θ)=-cos(θ+pi/2)	prove\:\sin(θ)=-\cos(θ+\frac{π}{2})
prove (sin(θ)+cos(θ))/(sin(θ))=1+cot(θ)	prove\:\frac{\sin(θ)+\cos(θ)}{\sin(θ)}=1+\cot(θ)
prove cos^2(x)(sec(x)+1)^2=(cos(x)+1)^2	prove\:\cos^{2}(x)(\sec(x)+1)^{2}=(\cos(x)+1)^{2}
prove sin^2(x)+cos(x^2)=1	prove\:\sin^{2}(x)+\cos(x^{2})=1
prove (cos(u))/(1+tan(u))-(sin(u))/(1+cot(u))=cos(u)-sin(u)	prove\:\frac{\cos(u)}{1+\tan(u)}-\frac{\sin(u)}{1+\cot(u)}=\cos(u)-\sin(u)
prove (sin(x)+cos(x))^2=1+2sin(x)	prove\:(\sin(x)+\cos(x))^{2}=1+2\sin(x)
prove csc(θ)= 1/(sec(θ))	prove\:\csc(θ)=\frac{1}{\sec(θ)}
prove cot(2x)+tan(x)=csc(2x)	prove\:\cot(2x)+\tan(x)=\csc(2x)
prove 2cos^2(x/2)-1=cos(x)	prove\:2\cos^{2}(\frac{x}{2})-1=\cos(x)
prove (csc(z))/(sec(z))=cot(z)	prove\:\frac{\csc(z)}{\sec(z)}=\cot(z)
prove (tan(θ)cot(θ))/(sec(θ))=cos(θ)	prove\:\frac{\tan(θ)\cot(θ)}{\sec(θ)}=\cos(θ)
prove (sin(x)+sin(3x))/(cos(x)-cos(3x))=cot(x)	prove\:\frac{\sin(x)+\sin(3x)}{\cos(x)-\cos(3x)}=\cot(x)
prove tan^2(b)-tan^2(b)sin^2(b)=sin^2(b)	prove\:\tan^{2}(b)-\tan^{2}(b)\sin^{2}(b)=\sin^{2}(b)
prove 2cos(x)sin(x)=sin(2x)	prove\:2\cos(x)\sin(x)=\sin(2x)
prove (cot(x)*sec(x))/(csc(x))=1	prove\:\frac{\cot(x)\cdot\:\sec(x)}{\csc(x)}=1
prove sin(x)+tan(x)=tan(x)(1+cos(x))	prove\:\sin(x)+\tan(x)=\tan(x)(1+\cos(x))
prove 3sin(x)cos(x)=3sin^2(x)cot(x)	prove\:3\sin(x)\cos(x)=3\sin^{2}(x)\cot(x)
prove 7cos(x)+7sin(x)tan(x)=7sec(x)	prove\:7\cos(x)+7\sin(x)\tan(x)=7\sec(x)
prove sin((3pi)/2-0)=-cos(0)	prove\:\sin(\frac{3π}{2}-0)=-\cos(0)
prove sin(x)+cos(2x)=4sin^2(x)-1	prove\:\sin(x)+\cos(2x)=4\sin^{2}(x)-1
prove (tan(3a))/(1+sec(3a))+(1+sec(3a))/(tan(3a))=2csc(3a)	prove\:\frac{\tan(3a)}{1+\sec(3a)}+\frac{1+\sec(3a)}{\tan(3a)}=2\csc(3a)
prove (sec(x)-cos(x))/(sin(x))=tan(x)	prove\:\frac{\sec(x)-\cos(x)}{\sin(x)}=\tan(x)
prove tan(-θ)=tan(θ)	prove\:\tan(-θ)=\tan(θ)
prove sec(x^2)+csc^2(x)=sec^2(x)csc^2(x)	prove\:\sec(x^{2})+\csc^{2}(x)=\sec^{2}(x)\csc^{2}(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 cos(x-y)=cos(y-x)	prove\:\cos(x-y)=\cos(y-x)
prove tan^2(a)=(sin^2(a))/(1-sin^2(a))	prove\:\tan^{2}(a)=\frac{\sin^{2}(a)}{1-\sin^{2}(a)}
prove (sec^2(x))/(csc^2(x))=tan^2(x)	prove\:\frac{\sec^{2}(x)}{\csc^{2}(x)}=\tan^{2}(x)
prove cos(4pi+x)=cos(x)	prove\:\cos(4π+x)=\cos(x)
prove 5cot^2(y)(sec^2(y)-1)=5	prove\:5\cot^{2}(y)(\sec^{2}(y)-1)=5
prove sin(x)cos(y)+sin(y)cos(x)=sin(x+y)	prove\:\sin(x)\cos(y)+\sin(y)\cos(x)=\sin(x+y)
prove (csc^2(x))/(sec^2(x))=cot^2(x)	prove\:\frac{\csc^{2}(x)}{\sec^{2}(x)}=\cot^{2}(x)
prove (sin(7x)-sin(5x))/(cos(7x)+cos(5x))=tan(x)	prove\:\frac{\sin(7x)-\sin(5x)}{\cos(7x)+\cos(5x)}=\tan(x)
prove tan(A+B)+tan(A-B)=((2sin(2A)))/((cos(2A)+cos(2B)))	prove\:\tan(A+B)+\tan(A-B)=\frac{(2\sin(2A))}{(\cos(2A)+\cos(2B))}
prove cos(3θ)=4cos^3(θ)-cos(θ)	prove\:\cos(3θ)=4\cos^{3}(θ)-\cos(θ)
prove cos^2(b)+cos^2(pi/2-b)=1	prove\:\cos^{2}(b)+\cos^{2}(\frac{π}{2}-b)=1
prove sec(x)-(sin(x))(tan(x))=cos(x)	prove\:\sec(x)-(\sin(x))(\tan(x))=\cos(x)
prove 1/(tan(θ))+tan(θ)=sec(θ)csc(θ)	prove\:\frac{1}{\tan(θ)}+\tan(θ)=\sec(θ)\csc(θ)
prove sec(x)-1/(sec(x))=sin(x)tan(x)	prove\:\sec(x)-\frac{1}{\sec(x)}=\sin(x)\tan(x)
prove (1+csc(b))/(cot(b)+cos(b))=sec(b)	prove\:\frac{1+\csc(b)}{\cot(b)+\cos(b)}=\sec(b)
prove (1+tan^2(θ))/(tan(θ))=sec(θ)csc(θ)	prove\:\frac{1+\tan^{2}(θ)}{\tan(θ)}=\sec(θ)\csc(θ)
prove (1-cos(2x))/(sin(x))=2sin(x)	prove\:\frac{1-\cos(2x)}{\sin(x)}=2\sin(x)
prove tan(θ)=sin(θ)sec(θ)	prove\:\tan(θ)=\sin(θ)\sec(θ)
prove sin^2(x)=1-cos(2x)	prove\:\sin^{2}(x)=1-\cos(2x)
prove 1-((cos^2(x))/(1+sin(x)))=sin(x)	prove\:1-(\frac{\cos^{2}(x)}{1+\sin(x)})=\sin(x)
prove sin(4a)=2sin(2a)cos(2a)	prove\:\sin(4a)=2\sin(2a)\cos(2a)
prove tan(x)=sec(x)sin(x)	prove\:\tan(x)=\sec(x)\sin(x)
prove sin(2D)=2cot(D)sin^2(D)	prove\:\sin(2D)=2\cot(D)\sin^{2}(D)
prove tan^2(pi/6)= 1/3	prove\:\tan^{2}(\frac{π}{6})=\frac{1}{3}
prove (1+csc^2(x))/(csc^2(x))=1+sin^2(x)	prove\:\frac{1+\csc^{2}(x)}{\csc^{2}(x)}=1+\sin^{2}(x)
prove (sin(a)+cos(a))^2-2sin(a)cos(a)=1	prove\:(\sin(a)+\cos(a))^{2}-2\sin(a)\cos(a)=1
prove cos(x)+sin(x)+tan(x)=sec(x)	prove\:\cos(x)+\sin(x)+\tan(x)=\sec(x)
prove sqrt(81-9(3sin(x))^2)=4sin(x)+8	prove\:\sqrt{81-9(3\sin(x))^{2}}=4\sin(x)+8
prove cot(x)*cos(x)+sin(x)=csc(x)	prove\:\cot(x)\cdot\:\cos(x)+\sin(x)=\csc(x)
prove (1-cos^2(a))*(1+tan^2(a))=tan^2(a)	prove\:(1-\cos^{2}(a))\cdot\:(1+\tan^{2}(a))=\tan^{2}(a)
prove csc(x)*tan(x)+sec(x)=2sec(x)	prove\:\csc(x)\cdot\:\tan(x)+\sec(x)=2\sec(x)
prove (cos(x)+sin(x))^2=1+2cos(x)sin(x)	prove\:(\cos(x)+\sin(x))^{2}=1+2\cos(x)\sin(x)
prove tan((5pi)/3)=-sqrt(3)	prove\:\tan(\frac{5π}{3})=-\sqrt{3}
prove sin(A)= 3/5	prove\:\sin(A)=\frac{3}{5}
prove (3+cos(4x))/4 =sin^4(x)+cos^4(x)	prove\:\frac{3+\cos(4x)}{4}=\sin^{4}(x)+\cos^{4}(x)

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