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Popular Trigonometry Problems

prove csc(θ)=cos(θ)cot(θ)+sin(θ)	prove\:\csc(θ)=\cos(θ)\cot(θ)+\sin(θ)
prove cos^4(x)+sin^2(x)cos^2(x)=cos^2(x)	prove\:\cos^{4}(x)+\sin^{2}(x)\cos^{2}(x)=\cos^{2}(x)
prove (tan(x)cos(x))/(sin(x))=1	prove\:\frac{\tan(x)\cos(x)}{\sin(x)}=1
prove ((sec^2(x)))/(tan(x))=sec(x)csc(x)	prove\:\frac{(\sec^{2}(x))}{\tan(x)}=\sec(x)\csc(x)
prove cot(θ)csc(θ)tan^2(θ)=sec(θ)	prove\:\cot(θ)\csc(θ)\tan^{2}(θ)=\sec(θ)
prove (cot(x)+cos(x))/(1+csc(x))=cos(x)	prove\:\frac{\cot(x)+\cos(x)}{1+\csc(x)}=\cos(x)
prove sin(z+pi/2)=cos(z)	prove\:\sin(z+\frac{π}{2})=\cos(z)
prove (sec(α))/(1-cos(α))=(sec(α)+1)/(sin^2(α))	prove\:\frac{\sec(α)}{1-\cos(α)}=\frac{\sec(α)+1}{\sin^{2}(α)}
prove 2csc(2x)=csc(x)sec(x)	prove\:2\csc(2x)=\csc(x)\sec(x)
prove 1/(sin(y)-1)-1/(sin(y)+1)=-2sec^2(y)	prove\:\frac{1}{\sin(y)-1}-\frac{1}{\sin(y)+1}=-2\sec^{2}(y)
prove cos(pi/4)=(sqrt(2))/2	prove\:\cos(\frac{π}{4})=\frac{\sqrt{2}}{2}
prove 7cot^2(y)(sec^2(y)-1)=7	prove\:7\cot^{2}(y)(\sec^{2}(y)-1)=7
prove cos^2(x)-sin^2(x)cos^2(x)=cos^4(x)	prove\:\cos^{2}(x)-\sin^{2}(x)\cos^{2}(x)=\cos^{4}(x)
prove sec^2(x)-tan(x)cot(x)=tan^2(x)	prove\:\sec^{2}(x)-\tan(x)\cot(x)=\tan^{2}(x)
prove 1/(csc^2(x))+cos^2(x)=1	prove\:\frac{1}{\csc^{2}(x)}+\cos^{2}(x)=1
prove 2cos^2(θ)-1=1-2sin^2(θ)	prove\:2\cos^{2}(θ)-1=1-2\sin^{2}(θ)
prove cot(x)=(csc(x))/(sec(x))	prove\:\cot(x)=\frac{\csc(x)}{\sec(x)}
prove 1/(1+sin(x))+1/(1-sin(x))=2+2tan^2(x)	prove\:\frac{1}{1+\sin(x)}+\frac{1}{1-\sin(x)}=2+2\tan^{2}(x)
prove tan(a)=(sin(a))/(cos(a))	prove\:\tan(a)=\frac{\sin(a)}{\cos(a)}
prove sec(2x)=(sec^2(x))/(1-tan^2(x))	prove\:\sec(2x)=\frac{\sec^{2}(x)}{1-\tan^{2}(x)}
prove 1-(cos^2(a))/(1+sin(a))=sin(a)	prove\:1-\frac{\cos^{2}(a)}{1+\sin(a)}=\sin(a)
prove (tan(x)csc(x))/(sec(x))=1	prove\:\frac{\tan(x)\csc(x)}{\sec(x)}=1
prove (sin(3x)-sin(5x))/(2cos(4x))=-sin(x)	prove\:\frac{\sin(3x)-\sin(5x)}{2\cos(4x)}=-\sin(x)
prove 2tan(θ)(1+cos(2θ))=2sin(2θ)	prove\:2\tan(θ)(1+\cos(2θ))=2\sin(2θ)
prove sec^2(x)-1=(sin^2(x))/(cos^2(x))	prove\:\sec^{2}(x)-1=\frac{\sin^{2}(x)}{\cos^{2}(x)}
prove tan(a)+cot(a)=2csc(2a)	prove\:\tan(a)+\cot(a)=2\csc(2a)
prove (sec^2(t))/(csc(t))=sec(t)tan(t)	prove\:\frac{\sec^{2}(t)}{\csc(t)}=\sec(t)\tan(t)
prove (sec(t)-1)/(tan(t))=(tan(t))/(sec(t)+1)	prove\:\frac{\sec(t)-1}{\tan(t)}=\frac{\tan(t)}{\sec(t)+1}
prove 3cos^2(x)-3sin^2(x)=3-6sin^2(x)	prove\:3\cos^{2}(x)-3\sin^{2}(x)=3-6\sin^{2}(x)
prove 1/((1+tan^2(x)))=cos^2(x)	prove\:\frac{1}{(1+\tan^{2}(x))}=\cos^{2}(x)
prove 1/(sec(θ)+tan(θ))=sec(θ)-tan(θ)	prove\:\frac{1}{\sec(θ)+\tan(θ)}=\sec(θ)-\tan(θ)
prove sec^4(x)= 1/(cos^4(x))	prove\:\sec^{4}(x)=\frac{1}{\cos^{4}(x)}
prove tan^2(x)+sec^2(x)=2sec^2(x)-1	prove\:\tan^{2}(x)+\sec^{2}(x)=2\sec^{2}(x)-1
prove 2cos^3(x)-cos(x)=(cos^2(x)-sin^2(x))/(sec(x))	prove\:2\cos^{3}(x)-\cos(x)=\frac{\cos^{2}(x)-\sin^{2}(x)}{\sec(x)}
prove (tan^2(x))/(sin^2(x))-1=tan^2(x)	prove\:\frac{\tan^{2}(x)}{\sin^{2}(x)}-1=\tan^{2}(x)
prove (cos(5x)-cos(3x))/(sin(5x)+sin(3x))=-tan(x)	prove\:\frac{\cos(5x)-\cos(3x)}{\sin(5x)+\sin(3x)}=-\tan(x)
prove 1/(cot^2(x)+1)=sin^2(x)	prove\:\frac{1}{\cot^{2}(x)+1}=\sin^{2}(x)
prove 1/(tan(x))=cot(x)	prove\:\frac{1}{\tan(x)}=\cot(x)
prove (1+tan(θ))/(cos(θ)+sin(θ))=sec(θ)	prove\:\frac{1+\tan(θ)}{\cos(θ)+\sin(θ)}=\sec(θ)
prove (cos(x))/(sec(x)+tan(x))=1-sin(x)	prove\:\frac{\cos(x)}{\sec(x)+\tan(x)}=1-\sin(x)
prove-tan(x)-(cos(x))/(sin(x)-1)=sec(x)	prove\:-\tan(x)-\frac{\cos(x)}{\sin(x)-1}=\sec(x)
prove tan(x)*sin(x)+cos(x)=sec(x)	prove\:\tan(x)\cdot\:\sin(x)+\cos(x)=\sec(x)
prove cos(θ)+cos(θ)tan^2(θ)=sec(θ)	prove\:\cos(θ)+\cos(θ)\tan^{2}(θ)=\sec(θ)
prove (cos(θ)+sin(θ))/(sin(θ))=1+cot(θ)	prove\:\frac{\cos(θ)+\sin(θ)}{\sin(θ)}=1+\cot(θ)
prove sec^2(x)-sin^2(x)sec^2(x)=1	prove\:\sec^{2}(x)-\sin^{2}(x)\sec^{2}(x)=1
prove tan(2a)-2tan(2a)sin^2(a)=sin(2a)	prove\:\tan(2a)-2\tan(2a)\sin^{2}(a)=\sin(2a)
prove tan(t)sin(t)=(sec^2(t)-1)/(sec(t))	prove\:\tan(t)\sin(t)=\frac{\sec^{2}(t)-1}{\sec(t)}
prove 2cos^2(x)=1+cos(2x)	prove\:2\cos^{2}(x)=1+\cos(2x)
prove 80=arcsin(45.6443*(sin(c))/(35))	prove\:80=\arcsin(45.6443\cdot\:\frac{\sin(c)}{35})
prove sin(0)csc(0)=1	prove\:\sin(0)\csc(0)=1
prove ((tan^2(x)))/(sec(x))=sin(x)tan(x)	prove\:\frac{(\tan^{2}(x))}{\sec(x)}=\sin(x)\tan(x)
prove cos(x)(1+tan(x))^2=sec(x)+2sin(x)	prove\:\cos(x)(1+\tan(x))^{2}=\sec(x)+2\sin(x)
prove cos(x)cot(x)= 1/(sin(x))-sin(x)	prove\:\cos(x)\cot(x)=\frac{1}{\sin(x)}-\sin(x)
prove tan(θ)=(sec(θ))/(csc(θ))	prove\:\tan(θ)=\frac{\sec(θ)}{\csc(θ)}
prove (sec(θ))/(csc^2(θ))=sec(θ)-cos(θ)	prove\:\frac{\sec(θ)}{\csc^{2}(θ)}=\sec(θ)-\cos(θ)
prove cos(3β)=cos(β)(cos^2(β)-3sin^2(β))	prove\:\cos(3β)=\cos(β)(\cos^{2}(β)-3\sin^{2}(β))
prove sec^2(θ)cot^2(θ)-1=cot^2(θ)	prove\:\sec^{2}(θ)\cot^{2}(θ)-1=\cot^{2}(θ)
prove 1-((sin^2(x)))/(1+cos(x))=cos(x)	prove\:1-\frac{(\sin^{2}(x))}{1+\cos(x)}=\cos(x)
prove cot(a)= 1/(tan(a))	prove\:\cot(a)=\frac{1}{\tan(a)}
prove cos(u)sec(u)-cos^2(u)=sin^2(u)	prove\:\cos(u)\sec(u)-\cos^{2}(u)=\sin^{2}(u)
prove (sec(θ))/(cot(θ)+tan(θ))=sin(θ)	prove\:\frac{\sec(θ)}{\cot(θ)+\tan(θ)}=\sin(θ)
prove sin^2(θ/2)=(1-cos(θ))/2	prove\:\sin^{2}(\frac{θ}{2})=\frac{1-\cos(θ)}{2}
prove (cos(θ)+1)/(sin(θ))=cot(θ)+csc(θ)	prove\:\frac{\cos(θ)+1}{\sin(θ)}=\cot(θ)+\csc(θ)
prove cos(2A)=2cos^2(A)-1	prove\:\cos(2A)=2\cos^{2}(A)-1
prove 2sin^2(3x)=1-cos(6x)	prove\:2\sin^{2}(3x)=1-\cos(6x)
prove sec^2(x)-1=(tan(x))/(cot(x))	prove\:\sec^{2}(x)-1=\frac{\tan(x)}{\cot(x)}
prove sec(θ)cos(θ)=1	prove\:\sec(θ)\cos(θ)=1
prove cot(θ)(cot(θ)+tan(θ))=csc^2(θ)	prove\:\cot(θ)(\cot(θ)+\tan(θ))=\csc^{2}(θ)
prove cos(pi/2+y)=-sin(y)	prove\:\cos(\frac{π}{2}+y)=-\sin(y)
prove-tan^2(x)+sec^2(x)=1	prove\:-\tan^{2}(x)+\sec^{2}(x)=1
prove tan(2θ)=(2cot(θ))/(cot^2(θ)-1)	prove\:\tan(2θ)=\frac{2\cot(θ)}{\cot^{2}(θ)-1}
prove csc(x)-tan(x/2)=cot(x)	prove\:\csc(x)-\tan(\frac{x}{2})=\cot(x)
prove cos(3x)-cos(x)=4cos^3(x)-4cos(x)	prove\:\cos(3x)-\cos(x)=4\cos^{3}(x)-4\cos(x)
prove cot^2(θ)-cos^2(θ)=cos^2(θ)cot^2(θ)	prove\:\cot^{2}(θ)-\cos^{2}(θ)=\cos^{2}(θ)\cot^{2}(θ)
prove (tan(A))/(sec(A))=sin(A)	prove\:\frac{\tan(A)}{\sec(A)}=\sin(A)
prove tan(8x)-tan(8x)tan^2(4x)=2tan(4x)	prove\:\tan(8x)-\tan(8x)\tan^{2}(4x)=2\tan(4x)
prove (sin^2(x))/(cos(x)+1)=1-cos(x)	prove\:\frac{\sin^{2}(x)}{\cos(x)+1}=1-\cos(x)
prove cot(2u)=(cot^2(u)-1)/(2cot(u))	prove\:\cot(2u)=\frac{\cot^{2}(u)-1}{2\cot(u)}
prove (sin(θ)csc(θ))/(cot(θ))=tan(θ)	prove\:\frac{\sin(θ)\csc(θ)}{\cot(θ)}=\tan(θ)
prove (sin(2x))/2 =sin(x)cos(x)	prove\:\frac{\sin(2x)}{2}=\sin(x)\cos(x)
prove sin(θ)=sin^3(θ)+cos^2(θ)sin(θ)	prove\:\sin(θ)=\sin^{3}(θ)+\cos^{2}(θ)\sin(θ)
prove (csc(θ)-cot(θ))/(sec(θ)-1)=cot(θ)	prove\:\frac{\csc(θ)-\cot(θ)}{\sec(θ)-1}=\cot(θ)
prove sin^2(z)+cos^2(z)=1	prove\:\sin^{2}(z)+\cos^{2}(z)=1
prove tan(x)sin(x)=cos(x)	prove\:\tan(x)\sin(x)=\cos(x)
prove cot(θ)= 1/(tan(θ))	prove\:\cot(θ)=\frac{1}{\tan(θ)}
prove cos^2(θ)tan^2(θ)=sin^2(θ)	prove\:\cos^{2}(θ)\tan^{2}(θ)=\sin^{2}(θ)
prove 1-cot(x)=sqrt(csc^2(x)-2cot(x))	prove\:1-\cot(x)=\sqrt{\csc^{2}(x)-2\cot(x)}
prove sin^2(x)+cot^2(x)sin^2(x)=1	prove\:\sin^{2}(x)+\cot^{2}(x)\sin^{2}(x)=1
prove (1-cos^2(θ))/(tan^2(θ))=cos^2(θ)	prove\:\frac{1-\cos^{2}(θ)}{\tan^{2}(θ)}=\cos^{2}(θ)
prove tan^2(θ)cos^2(θ)=sin^2(θ)	prove\:\tan^{2}(θ)\cos^{2}(θ)=\sin^{2}(θ)
prove (csc^2(x))/(cot^2(x))=1+tan^2(x)	prove\:\frac{\csc^{2}(x)}{\cot^{2}(x)}=1+\tan^{2}(x)
prove sin(x/2)=sqrt((1+cos(x))/2)	prove\:\sin(\frac{x}{2})=\sqrt{\frac{1+\cos(x)}{2}}
prove (tan(a))/(sec(a))=sin(a)	prove\:\frac{\tan(a)}{\sec(a)}=\sin(a)
prove 1+1/(tan^2(θ))= 1/(sin^2(θ))	prove\:1+\frac{1}{\tan^{2}(θ)}=\frac{1}{\sin^{2}(θ)}
prove sin(x)+cos(x)=0	prove\:\sin(x)+\cos(x)=0
prove (sec^2(x)-1)/(sin^2(x))=sec^2(x)	prove\:\frac{\sec^{2}(x)-1}{\sin^{2}(x)}=\sec^{2}(x)
prove (1+sec(β))/(tan(β)+sin(β))=csc(β)	prove\:\frac{1+\sec(β)}{\tan(β)+\sin(β)}=\csc(β)
prove sin^2(x)*(1+cot^2(x))=1	prove\:\sin^{2}(x)\cdot\:(1+\cot^{2}(x))=1
prove 3sec(x)-3cos(x)=3sin(x)tan(x)	prove\:3\sec(x)-3\cos(x)=3\sin(x)\tan(x)
prove 1+tan^2(a)= 1/(cos^2(a))	prove\:1+\tan^{2}(a)=\frac{1}{\cos^{2}(a)}

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