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Problemas populares de Trigonometría

verificar 2cot^2(A)sin^2(A)=1+cos(2A)	prove\:2\cot^{2}(A)\sin^{2}(A)=1+\cos(2A)
verificar cos(pi/8)=cos((pi/4)/2)	prove\:\cos(\frac{π}{8})=\cos(\frac{\frac{π}{4}}{2})
verificar sin(x)+cos(x)=cos(x)(1+tan(x))	prove\:\sin(x)+\cos(x)=\cos(x)(1+\tan(x))
verificar (sin(x))/(sin(2x))= 1/(2cos(x))	prove\:\frac{\sin(x)}{\sin(2x)}=\frac{1}{2\cos(x)}
verificar cot(θ)sec^2(θ)-cot(θ)=tan(θ)	prove\:\cot(θ)\sec^{2}(θ)-\cot(θ)=\tan(θ)
verificar sqrt(2)cos(x-pi/4)=cos(x)+sin(x)	prove\:\sqrt{2}\cos(x-\frac{π}{4})=\cos(x)+\sin(x)
verificar cos^4(4x)-sin^4(4x)=cos(8x)	prove\:\cos^{4}(4x)-\sin^{4}(4x)=\cos(8x)
verificar (cos^2(x)-1)(tan^2(x)+1)=-tan^2(x)	prove\:(\cos^{2}(x)-1)(\tan^{2}(x)+1)=-\tan^{2}(x)
verificar 7csc^2(θ)-5cot^2(θ)=2csc^2(θ)+5	prove\:7\csc^{2}(θ)-5\cot^{2}(θ)=2\csc^{2}(θ)+5
verificar cos(θ)=(cot(θ))/(csc(θ))	prove\:\cos(θ)=\frac{\cot(θ)}{\csc(θ)}
verificar (cos(u))/(1-sin(u))=sec(u)+tan(u)	prove\:\frac{\cos(u)}{1-\sin(u)}=\sec(u)+\tan(u)
verificar cos(x-(3pi)/2)=-sin(x)	prove\:\cos(x-\frac{3π}{2})=-\sin(x)
verificar (sec^2(x))/(2-sec^2(x))=sec(2x)	prove\:\frac{\sec^{2}(x)}{2-\sec^{2}(x)}=\sec(2x)
verificar (cot(x)tan(x))/(cos(x))=sec(x)	prove\:\frac{\cot(x)\tan(x)}{\cos(x)}=\sec(x)
verificar (sin(θ))/(cos(θ))=tan(θ)	prove\:\frac{\sin(θ)}{\cos(θ)}=\tan(θ)
verificar cos(x)tan(x)csc(x)=1	prove\:\cos(x)\tan(x)\csc(x)=1
verificar sin(6x)tan(3x)=2sin^2(3x)	prove\:\sin(6x)\tan(3x)=2\sin^{2}(3x)
verificar cos(θ)cot(θ)+sin^2(θ)csc(θ)=csc(θ)	prove\:\cos(θ)\cot(θ)+\sin^{2}(θ)\csc(θ)=\csc(θ)
verificar sin^2(x)sec^2(x)+1=sec^2(x)	prove\:\sin^{2}(x)\sec^{2}(x)+1=\sec^{2}(x)
verificar cos(a+b)-cos(a-b)=-2sin(a)sin(b)	prove\:\cos(a+b)-\cos(a-b)=-2\sin(a)\sin(b)
verificar (tan(β)+sec(β))(1-sin(β))=cos(β)	prove\:(\tan(β)+\sec(β))(1-\sin(β))=\cos(β)
verificar sin(α+β)=sin(α)cos(β)+sin(β)cos(α)	prove\:\sin(α+β)=\sin(α)\cos(β)+\sin(β)\cos(α)
verificar sin(x)=(tan(x))/(sec(x))	prove\:\sin(x)=\frac{\tan(x)}{\sec(x)}
verificar 2-sec^2(z)=1-tan^2(z)	prove\:2-\sec^{2}(z)=1-\tan^{2}(z)
verificar-cos(-x)+sec(x)=tan(x)sin(x)	prove\:-\cos(-x)+\sec(x)=\tan(x)\sin(x)
verificar 1/(1-tan^2(θ))+1/(1-cot^2(θ))=1	prove\:\frac{1}{1-\tan^{2}(θ)}+\frac{1}{1-\cot^{2}(θ)}=1
verificar 1=sec^2(x)-tan^2(x)	prove\:1=\sec^{2}(x)-\tan^{2}(x)
verificar (sec^2(x)-6tan(x)+7)/(sec^2(x)-5)=(tan(x)-4)/(tan(x)+2)	prove\:\frac{\sec^{2}(x)-6\tan(x)+7}{\sec^{2}(x)-5}=\frac{\tan(x)-4}{\tan(x)+2}
verificar 1-cos(x)=2sin^2(x/2)	prove\:1-\cos(x)=2\sin^{2}(\frac{x}{2})
verificar cos(3A)=4cos^3(A)-3cos(A)	prove\:\cos(3A)=4\cos^{3}(A)-3\cos(A)
verificar sin(a)cot(a)=cos(a)	prove\:\sin(a)\cot(a)=\cos(a)
verificar cos(3θ)=cos^3(θ)-3sin^2(θ)cos(θ)	prove\:\cos(3θ)=\cos^{3}(θ)-3\sin^{2}(θ)\cos(θ)
verificar csc^6(x)-cot^6(x)=1+3csc^2(x)cot^2(x)	prove\:\csc^{6}(x)-\cot^{6}(x)=1+3\csc^{2}(x)\cot^{2}(x)
verificar (sin(x)+cos(x))^2=1+sin^2(x)	prove\:(\sin(x)+\cos(x))^{2}=1+\sin^{2}(x)
verificar cos^2(B)-sin^2(B)=2cos^2(B)-1	prove\:\cos^{2}(B)-\sin^{2}(B)=2\cos^{2}(B)-1
verificar 1/(1+sin(x))=(1-sin(x))/(cos^2(x))	prove\:\frac{1}{1+\sin(x)}=\frac{1-\sin(x)}{\cos^{2}(x)}
verificar csc^2(x)cos^2(x)= 1/(tan^2(x))	prove\:\csc^{2}(x)\cos^{2}(x)=\frac{1}{\tan^{2}(x)}
verificar cot(t)tan(t)=1	prove\:\cot(t)\tan(t)=1
verificar 1+tan^2(t)=sec^2(t)	prove\:1+\tan^{2}(t)=\sec^{2}(t)
verificar sec^2(x)=(csc(x))/(csc(x)-sin(x))	prove\:\sec^{2}(x)=\frac{\csc(x)}{\csc(x)-\sin(x)}
verificar (cos(θ))/(sin(θ))=cot(θ)	prove\:\frac{\cos(θ)}{\sin(θ)}=\cot(θ)
verificar (cot^2(θ))/(csc(θ))=csc(θ)-sin(θ)	prove\:\frac{\cot^{2}(θ)}{\csc(θ)}=\csc(θ)-\sin(θ)
verificar cos(4x)=2cos^2(2x)-1	prove\:\cos(4x)=2\cos^{2}(2x)-1
verificar (csc(0)+sec(0))/(tan(0)+1)=csc(0)	prove\:\frac{\csc(0)+\sec(0)}{\tan(0)+1}=\csc(0)
verificar-cos(x)tan(x)=-sin(x)	prove\:-\cos(x)\tan(x)=-\sin(x)
verificar (sin(2a))/(1-cos(2a))=cot(a)	prove\:\frac{\sin(2a)}{1-\cos(2a)}=\cot(a)
verificar tan(x)cot(x)=sec(x)csc(x)	prove\:\tan(x)\cot(x)=\sec(x)\csc(x)
verificar (cos(3x)-cos(7x))/(sin(3x)+sin(7x))=tan(2x)	prove\:\frac{\cos(3x)-\cos(7x)}{\sin(3x)+\sin(7x)}=\tan(2x)
verificar sin(x)sec(x)= 1/(cos(x)csc(x))	prove\:\sin(x)\sec(x)=\frac{1}{\cos(x)\csc(x)}
verificar 1+tan(x)=sec(x)	prove\:1+\tan(x)=\sec(x)
verificar 2sin^2(θ)-1=sin^2(θ)-cos^2(θ)	prove\:2\sin^{2}(θ)-1=\sin^{2}(θ)-\cos^{2}(θ)
verificar (1+cot(x))/(csc(x))=sin(x)+cos(x)	prove\:\frac{1+\cot(x)}{\csc(x)}=\sin(x)+\cos(x)
verificar (1+tan^2(x))cos(x)=sec(x)	prove\:(1+\tan^{2}(x))\cos(x)=\sec(x)
verificar (sec^2(θ)-1)/(tan(θ))=tan(θ)	prove\:\frac{\sec^{2}(θ)-1}{\tan(θ)}=\tan(θ)
verificar (tan(β))/(sec(β))=sin(β)	prove\:\frac{\tan(β)}{\sec(β)}=\sin(β)
verificar cos^2(x)cot(x)=cot(x)-sin(x)cos(x)	prove\:\cos^{2}(x)\cot(x)=\cot(x)-\sin(x)\cos(x)
verificar 1-cos(x)=(sin^2(x))/(1+cos(x))	prove\:1-\cos(x)=\frac{\sin^{2}(x)}{1+\cos(x)}
verificar 2/(cos^2(x))=2sec^2(x)	prove\:\frac{2}{\cos^{2}(x)}=2\sec^{2}(x)
verificar (1-cos(x))(1+sec(x))=-1	prove\:(1-\cos(x))(1+\sec(x))=-1
verificar 2cos^2(a)=(1+sec(2a))cos(2a)	prove\:2\cos^{2}(a)=(1+\sec(2a))\cos(2a)
verificar sec(a)-sin(a)tan(a)=cos(a)	prove\:\sec(a)-\sin(a)\tan(a)=\cos(a)
verificar (cos(t))/(sec(t)-tan(t))=1+sin(t)	prove\:\frac{\cos(t)}{\sec(t)-\tan(t)}=1+\sin(t)
verificar sin((13pi)/2+x)=cos(x)	prove\:\sin(\frac{13π}{2}+x)=\cos(x)
verificar tan^2(-θ)+1=sec^2(θ)	prove\:\tan^{2}(-θ)+1=\sec^{2}(θ)
verificar (1+csc(β))/(cot(β)+cos(β))=sec(β)	prove\:\frac{1+\csc(β)}{\cot(β)+\cos(β)}=\sec(β)
verificar (1-cos(b))(1+cos(b))= 1/(csc^2(b))	prove\:(1-\cos(b))(1+\cos(b))=\frac{1}{\csc^{2}(b)}
verificar sin(θ-pi/2)=cos(pi+θ)	prove\:\sin(θ-\frac{π}{2})=\cos(π+θ)
verificar 1/(cot(θ))=(sec^2(θ)-1)/(tan(θ))	prove\:\frac{1}{\cot(θ)}=\frac{\sec^{2}(θ)-1}{\tan(θ)}
verificar (cos(x))/(sin(x)+1)=sec(x)-tan(x)	prove\:\frac{\cos(x)}{\sin(x)+1}=\sec(x)-\tan(x)
verificar tan(-sqrt(7))=tan(pi-sqrt(7))	prove\:\tan(-\sqrt{7})=\tan(π-\sqrt{7})
verificar sin(x)-1=cos(x)	prove\:\sin(x)-1=\cos(x)
verificar 25sec^2(5x)=25+25tan^2(5x)	prove\:25\sec^{2}(5x)=25+25\tan^{2}(5x)
verificar tan(x)+cot(x)=1	prove\:\tan(x)+\cot(x)=1
verificar tan(a)=(cos(a))/(sin(a)cot^2(a))	prove\:\tan(a)=\frac{\cos(a)}{\sin(a)\cot^{2}(a)}
verificar sin(θ-pi)=-sin(θ)	prove\:\sin(θ-π)=-\sin(θ)
verificar csc(u)sin(u)-sin^2(u)=cos^2(u)	prove\:\csc(u)\sin(u)-\sin^{2}(u)=\cos^{2}(u)
verificar (sin(x)cos(x))/(1-cos^2(x))=cot(x)	prove\:\frac{\sin(x)\cos(x)}{1-\cos^{2}(x)}=\cot(x)
verificar sin(2A)-tan(A)=tan(A)cos(2A)	prove\:\sin(2A)-\tan(A)=\tan(A)\cos(2A)
verificar cot^2(x)-cot^2(x)cos^2(x)=cos^2(x)	prove\:\cot^{2}(x)-\cot^{2}(x)\cos^{2}(x)=\cos^{2}(x)
verificar tan(x-pi)=tan(x)	prove\:\tan(x-π)=\tan(x)
verificar 1-2sin^2(θ/2)=2cos^2(θ/2)-1	prove\:1-2\sin^{2}(\frac{θ}{2})=2\cos^{2}(\frac{θ}{2})-1
verificar (1-sin^2(x))sec^2(x)=1	prove\:(1-\sin^{2}(x))\sec^{2}(x)=1
verificar tan(x)sin(x)=1-cos(x)	prove\:\tan(x)\sin(x)=1-\cos(x)
verificar (tan(x))/(sec(x)-cos(x))=csc(x)	prove\:\frac{\tan(x)}{\sec(x)-\cos(x)}=\csc(x)
verificar 1+sin(θ)=(cos^2(θ))/(1-sin(θ))	prove\:1+\sin(θ)=\frac{\cos^{2}(θ)}{1-\sin(θ)}
verificar (2sin^2(t))/(tan^2(t))=2cos^2(t)	prove\:\frac{2\sin^{2}(t)}{\tan^{2}(t)}=2\cos^{2}(t)
verificar tan(2θ)=(2tan(θ))/((1-tan(2θ)))	prove\:\tan(2θ)=\frac{2\tan(θ)}{(1-\tan(2θ))}
verificar tan(A)*cot(A)=1	prove\:\tan(A)\cdot\:\cot(A)=1
verificar 1/(csc(y)-cot(y))=csc(y)+cot(y)	prove\:\frac{1}{\csc(y)-\cot(y)}=\csc(y)+\cot(y)
verificar (tan^2(x))/(sec^2(x))=sin^2(x)	prove\:\frac{\tan^{2}(x)}{\sec^{2}(x)}=\sin^{2}(x)
verificar cot^2(x)=1+csc^2(x)	prove\:\cot^{2}(x)=1+\csc^{2}(x)
verificar tan^4(t)+tan^2(t)=sec^4(t)-sec^2(t)	prove\:\tan^{4}(t)+\tan^{2}(t)=\sec^{4}(t)-\sec^{2}(t)
verificar tan^2(x)cos^2(x)=sin^2(x)	prove\:\tan^{2}(x)\cos^{2}(x)=\sin^{2}(x)
verificar (tan^2(x)+1)/(1-sin^2(x))=sec^4(x)	prove\:\frac{\tan^{2}(x)+1}{1-\sin^{2}(x)}=\sec^{4}(x)
verificar tan(A)=(sec(A))/(csc(A))	prove\:\tan(A)=\frac{\sec(A)}{\csc(A)}
verificar csc(-x)=-csc(x)	prove\:\csc(-x)=-\csc(x)
verificar sin(β)+cos(β)cot(β)=csc(β)	prove\:\sin(β)+\cos(β)\cot(β)=\csc(β)
verificar cos((3pi)/2+x)=-cos(x)	prove\:\cos(\frac{3π}{2}+x)=-\cos(x)
verificar sec(x)+tan(x)= 1/(sec(x)+tan(x))	prove\:\sec(x)+\tan(x)=\frac{1}{\sec(x)+\tan(x)}
verificar csc(x)= 1/(cos(x))	prove\:\csc(x)=\frac{1}{\cos(x)}

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