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Problemas populares de Trigonometría

verificar csc^2(x)=cot^2(x)+1	prove\:\csc^{2}(x)=\cot^{2}(x)+1
verificar tan(x)-1=sec(x)(sin(x)-cos(x))	prove\:\tan(x)-1=\sec(x)(\sin(x)-\cos(x))
verificar (1-cos^2(x))/(tan^2(x))=cos^2(x)	prove\:\frac{1-\cos^{2}(x)}{\tan^{2}(x)}=\cos^{2}(x)
verificar (sin(x)+1)/(sin(x))=1+csc(x)	prove\:\frac{\sin(x)+1}{\sin(x)}=1+\csc(x)
verificar 1/(tan(x))=(cos(x))/(sin(x))	prove\:\frac{1}{\tan(x)}=\frac{\cos(x)}{\sin(x)}
verificar sin(x)-cos(x)=sqrt(1-sin(2x))	prove\:\sin(x)-\cos(x)=\sqrt{1-\sin(2x)}
verificar 9sec^2(x)-5tan^2(x)=5+4sec^2(x)	prove\:9\sec^{2}(x)-5\tan^{2}(x)=5+4\sec^{2}(x)
verificar (1-cos^2(x))cot(x)=sin^2(x)cot(x)	prove\:(1-\cos^{2}(x))\cot(x)=\sin^{2}(x)\cot(x)
verificar sin(3A)=3sin(A)-4sin^3(A)	prove\:\sin(3A)=3\sin(A)-4\sin^{3}(A)
verificar cot^4(x)+cot^2(x)=cot^2(x)csc^2(x)	prove\:\cot^{4}(x)+\cot^{2}(x)=\cot^{2}(x)\csc^{2}(x)
verificar cot^3(x)=cot(x)(csc^2(x)-1)	prove\:\cot^{3}(x)=\cot(x)(\csc^{2}(x)-1)
verificar sin(2a)=(2tan(a))/(1+tan^2(a))	prove\:\sin(2a)=\frac{2\tan(a)}{1+\tan^{2}(a)}
verificar 10sec^2(θ)-4tan^2(θ)=4+6sec^2(θ)	prove\:10\sec^{2}(θ)-4\tan^{2}(θ)=4+6\sec^{2}(θ)
verificar tan(x)=((1-cos(2x)))/(sin(2x))	prove\:\tan(x)=\frac{(1-\cos(2x))}{\sin(2x)}
verificar sin^2(a)-cos^2(a)=1-2cos^2(a)	prove\:\sin^{2}(a)-\cos^{2}(a)=1-2\cos^{2}(a)
verificar tan(2A)-2tan(2A)sin^2(A)=sin(2A)	prove\:\tan(2A)-2\tan(2A)\sin^{2}(A)=\sin(2A)
verificar 1/(tan(x)csc(x))=cos(x)	prove\:\frac{1}{\tan(x)\csc(x)}=\cos(x)
verificar tan(4θ)+tan(2θ)=sec(4θ)-sec(2θ)	prove\:\tan(4θ)+\tan(2θ)=\sec(4θ)-\sec(2θ)
verificar tan^2(x)csc^2(x)-1=tan^2(x)	prove\:\tan^{2}(x)\csc^{2}(x)-1=\tan^{2}(x)
verificar sin^2(x)= 1/(csc^2(x))	prove\:\sin^{2}(x)=\frac{1}{\csc^{2}(x)}
verificar (cot(4u)-1)/(cot(4u)+1)=(1-tan(4u))/(1+tan(4u))	prove\:\frac{\cot(4u)-1}{\cot(4u)+1}=\frac{1-\tan(4u)}{1+\tan(4u)}
verificar sin(-x)=sin(x-pi)	prove\:\sin(-x)=\sin(x-π)
verificar 1/(sec(θ)-tan(θ))=sec(θ)+tan(θ)	prove\:\frac{1}{\sec(θ)-\tan(θ)}=\sec(θ)+\tan(θ)
verificar sin(4a)=4sin(a)cos(a)cos(2a)	prove\:\sin(4a)=4\sin(a)\cos(a)\cos(2a)
verificar 3cos^2(x)-2=1-3sin^2(x)	prove\:3\cos^{2}(x)-2=1-3\sin^{2}(x)
verificar tan(a/2)=(sin(a))/(1+cos(a))	prove\:\tan(\frac{a}{2})=\frac{\sin(a)}{1+\cos(a)}
verificar 2cot(θ)=csc^2(θ)sin(2θ)	prove\:2\cot(θ)=\csc^{2}(θ)\sin(2θ)
verificar cos(3t)=cos^3(t)-3sin^2(t)cos(t)	prove\:\cos(3t)=\cos^{3}(t)-3\sin^{2}(t)\cos(t)
verificar sin^2(x)sec(x)csc(x)=tan(x)	prove\:\sin^{2}(x)\sec(x)\csc(x)=\tan(x)
verificar 4sin(x)cos(x)+1=2sin(2x)+1	prove\:4\sin(x)\cos(x)+1=2\sin(2x)+1
verificar 1-(tan(θ)cos(θ))/(csc(θ))=cos^2(θ)	prove\:1-\frac{\tan(θ)\cos(θ)}{\csc(θ)}=\cos^{2}(θ)
verificar sin(x)cos(x)tan(x)=sin^2(x)	prove\:\sin(x)\cos(x)\tan(x)=\sin^{2}(x)
verificar cot^6(x)=cot^4(x)csc^2(x)-cot^4(x)	prove\:\cot^{6}(x)=\cot^{4}(x)\csc^{2}(x)-\cot^{4}(x)
verificar tan^2(θ)(csc^2(θ)-1)=1	prove\:\tan^{2}(θ)(\csc^{2}(θ)-1)=1
verificar cos(x)(tan(x)+1)=sin(x)+cos(x)	prove\:\cos(x)(\tan(x)+1)=\sin(x)+\cos(x)
verificar tan^2(x)+sec^2(x)=1+2tan^2(x)	prove\:\tan^{2}(x)+\sec^{2}(x)=1+2\tan^{2}(x)
verificar (sin(2a))/(1+cos(2a))=tan(a)	prove\:\frac{\sin(2a)}{1+\cos(2a)}=\tan(a)
verificar tan(x)=tan(x+pi)	prove\:\tan(x)=\tan(x+π)
verificar 1+csc(a)=csc(a)(1+sin(a))	prove\:1+\csc(a)=\csc(a)(1+\sin(a))
verificar 1+cot(θ)=csc(θ)(cos(θ)+sin(θ))	prove\:1+\cot(θ)=\csc(θ)(\cos(θ)+\sin(θ))
verificar (1+cos(2x))/(sin^2(x))=2cot^2(x)	prove\:\frac{1+\cos(2x)}{\sin^{2}(x)}=2\cot^{2}(x)
verificar (cos(a))/(cot(a))=sin(a)	prove\:\frac{\cos(a)}{\cot(a)}=\sin(a)
verificar tan(θ)+cot(θ)= 2/(sin(2θ))	prove\:\tan(θ)+\cot(θ)=\frac{2}{\sin(2θ)}
verificar (csc(θ))/(sin(θ))=csc^2(θ)	prove\:\frac{\csc(θ)}{\sin(θ)}=\csc^{2}(θ)
verificar 2sin(2x)=4sin(x)cos(x)	prove\:2\sin(2x)=4\sin(x)\cos(x)
verificar (sin(x))(csc(x)-sin(x))=cos^2(x)	prove\:(\sin(x))(\csc(x)-\sin(x))=\cos^{2}(x)
verificar tan(x)+cot(x)-sec(x)csc(x)=0	prove\:\tan(x)+\cot(x)-\sec(x)\csc(x)=0
verificar (1-sin(x))/(sec(x))=(cos^3(x))/(1+sin(x))	prove\:\frac{1-\sin(x)}{\sec(x)}=\frac{\cos^{3}(x)}{1+\sin(x)}
verificar (1+cos(θ))(csc(θ)-cot(θ))=sin(θ)	prove\:(1+\cos(θ))(\csc(θ)-\cot(θ))=\sin(θ)
verificar cos(2α)=-1+2/(1+tan^2(α))	prove\:\cos(2α)=-1+\frac{2}{1+\tan^{2}(α)}
verificar (1+sec(x))(csc(x)-cot(x))=tan(x)	prove\:(1+\sec(x))(\csc(x)-\cot(x))=\tan(x)
verificar 2-csc^2(z)=1-cot^2(z)	prove\:2-\csc^{2}(z)=1-\cot^{2}(z)
verificar sin(x)tan(x)=(1+cos^2(x))/(cos(x))	prove\:\sin(x)\tan(x)=\frac{1+\cos^{2}(x)}{\cos(x)}
verificar tan(t)sec(t)=(sec^2(t)-1)/(sin(t))	prove\:\tan(t)\sec(t)=\frac{\sec^{2}(t)-1}{\sin(t)}
verificar cos(2x)=cos^4(x)-sin^4(x)	prove\:\cos(2x)=\cos^{4}(x)-\sin^{4}(x)
verificar csc(pi/2-u)=sec(u)	prove\:\csc(\frac{π}{2}-u)=\sec(u)
verificar-2sin(k-l)sin(k+l)=cos(2k)-cos(2l)	prove\:-2\sin(k-l)\sin(k+l)=\cos(2k)-\cos(2l)
verificar 2tan(2x)sin^2(x)=tan(2x)-sin(2x)	prove\:2\tan(2x)\sin^{2}(x)=\tan(2x)-\sin(2x)
verificar tan^2(x)+sec^2(x)=cot^2(x)	prove\:\tan^{2}(x)+\sec^{2}(x)=\cot^{2}(x)
verificar csc(x)-1=(1-sin(x))/(sin(x))	prove\:\csc(x)-1=\frac{1-\sin(x)}{\sin(x)}
verificar tan(x)sin(x)=(sec^2(x)-1)/(sec(x))	prove\:\tan(x)\sin(x)=\frac{\sec^{2}(x)-1}{\sec(x)}
verificar cos(θ-60)+cos(θ+60)=cos(θ)	prove\:\cos(θ-60^{\circ\:})+\cos(θ+60^{\circ\:})=\cos(θ)
verificar tan(2A)=(2tan(A))/(1-tan^2(A))	prove\:\tan(2A)=\frac{2\tan(A)}{1-\tan^{2}(A)}
verificar sin(x)-csc(x)=(-cos^2(x))/(sin(x))	prove\:\sin(x)-\csc(x)=\frac{-\cos^{2}(x)}{\sin(x)}
verificar sec^2(x)-sec^2(x)cos^2(x)=tan^2(x)	prove\:\sec^{2}(x)-\sec^{2}(x)\cos^{2}(x)=\tan^{2}(x)
verificar 1/(1-cos^2(x))=1+cot^2(x)	prove\:\frac{1}{1-\cos^{2}(x)}=1+\cot^{2}(x)
verificar 2/(tan(x)+cot(x))=sin(2x)	prove\:\frac{2}{\tan(x)+\cot(x)}=\sin(2x)
verificar sin(x)tan(x)sec(x)=sec^2(x)-1	prove\:\sin(x)\tan(x)\sec(x)=\sec^{2}(x)-1
verificar tan^4(k)-sec^4(k)=1-2sec^2(k)	prove\:\tan^{4}(k)-\sec^{4}(k)=1-2\sec^{2}(k)
verificar tan^2(x)+5=sec^2(x)+4	prove\:\tan^{2}(x)+5=\sec^{2}(x)+4
verificar 1-tan^4(x)=2sec^2(x)-sec^4(x)	prove\:1-\tan^{4}(x)=2\sec^{2}(x)-\sec^{4}(x)
verificar sin(pi)=sin(-pi)	prove\:\sin(π)=\sin(-π)
verificar csc^2(x)+2cot(x)=(1+cot(x))^2	prove\:\csc^{2}(x)+2\cot(x)=(1+\cot(x))^{2}
verificar csc(t)cot(t)=(1+cot^2(t))/(sec(t))	prove\:\csc(t)\cot(t)=\frac{1+\cot^{2}(t)}{\sec(t)}
verificar csc(a)sec(a)=2csc(2a)	prove\:\csc(a)\sec(a)=2\csc(2a)
verificar tan^2(x/2)=(sec(x)-1)/(sec(x)+1)	prove\:\tan^{2}(\frac{x}{2})=\frac{\sec(x)-1}{\sec(x)+1}
verificar tan^2(2x)+1=sec^2(2x)	prove\:\tan^{2}(2x)+1=\sec^{2}(2x)
verificar sin(4θ)=4sin(θ)cos(θ)cos(2θ)	prove\:\sin(4θ)=4\sin(θ)\cos(θ)\cos(2θ)
verificar sin^9(x)=(1-cos^2(x))^4sin(x)	prove\:\sin^{9}(x)=(1-\cos^{2}(x))^{4}\sin(x)
verificar csc^2(θ)=1-cot^2(θ)	prove\:\csc^{2}(θ)=1-\cot^{2}(θ)
verificar 1-cot(x)=sqrt((1-cot^2(x)))	prove\:1-\cot(x)=\sqrt{(1-\cot^{2}(x))}
verificar arccos(-x)=arccos(x)	prove\:\arccos(-x)=\arccos(x)
verificar sec^2(x)csc(x)=csc(x)+sec(x)tan(x)	prove\:\sec^{2}(x)\csc(x)=\csc(x)+\sec(x)\tan(x)
verificar sin(t)(csc(t)-sin(t))=cos^2(t)	prove\:\sin(t)(\csc(t)-\sin(t))=\cos^{2}(t)
verificar (sin(θ)+sin(3θ))/(cos(θ)+cos(3θ))=tan(2θ)	prove\:\frac{\sin(θ)+\sin(3θ)}{\cos(θ)+\cos(3θ)}=\tan(2θ)
verificar 1+cos((3pi)/4)=1-sin((3pi)/4)	prove\:1+\cos(\frac{3π}{4})=1-\sin(\frac{3π}{4})
verificar cos(90-x)=sin(x)	prove\:\cos(90^{\circ\:}-x)=\sin(x)
verificar sin((7pi)/6+x)-cos((2pi)/3+x)=0	prove\:\sin(\frac{7π}{6}+x)-\cos(\frac{2π}{3}+x)=0
verificar (1+cos(a))(1-cos(a))=sin^2(a)	prove\:(1+\cos(a))(1-\cos(a))=\sin^{2}(a)
verificar csc(θ)-cos(θ)cot(θ)=sin(θ)	prove\:\csc(θ)-\cos(θ)\cot(θ)=\sin(θ)
verificar sin(x+pi/3)+sin(x-pi/3)=sin(x)	prove\:\sin(x+\frac{π}{3})+\sin(x-\frac{π}{3})=\sin(x)
verificar tan(u)(csc(u)-sin(u))=cos(u)	prove\:\tan(u)(\csc(u)-\sin(u))=\cos(u)
verificar sin(x-y)+sin(x+y)=2cos(y)sin(x)	prove\:\sin(x-y)+\sin(x+y)=2\cos(y)\sin(x)
verificar (csc^2(x)-1)sin(x)=cot^2(x)sin(x)	prove\:(\csc^{2}(x)-1)\sin(x)=\cot^{2}(x)\sin(x)
verificar 1-2sin^2(x)+sin^4(x)=cos^4(x)	prove\:1-2\sin^{2}(x)+\sin^{4}(x)=\cos^{4}(x)
verificar (3sin^2(t))/(tan^2(t))=3cos^2(t)	prove\:\frac{3\sin^{2}(t)}{\tan^{2}(t)}=3\cos^{2}(t)
verificar 1/(tan^2(θ))=1+cot^2(θ)	prove\:\frac{1}{\tan^{2}(θ)}=1+\cot^{2}(θ)
verificar cos((4pi)/3)=-1/2	prove\:\cos(\frac{4π}{3})=-\frac{1}{2}
verificar (sin(3θ))/(sin(θ))=3-4sin^2(θ)	prove\:\frac{\sin(3θ)}{\sin(θ)}=3-4\sin^{2}(θ)
verificar tan(pi-θ)=tan(θ)	prove\:\tan(π-θ)=\tan(θ)

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