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Problemas populares Trigonometría

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 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 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 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 cos(3t)=cos^3(t)-3sin^2(t)cos(t)	prove\:\cos(3t)=\cos^{3}(t)-3\sin^{2}(t)\cos(t)
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 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 1+csc(a)=csc(a)(1+sin(a))	prove\:1+\csc(a)=\csc(a)(1+\sin(a))
verificar (1+cos(2x))/(sin^2(x))=2cot^2(x)	prove\:\frac{1+\cos(2x)}{\sin^{2}(x)}=2\cot^{2}(x)
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 (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 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 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 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)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 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(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(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 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 tan(u)(csc(u)-sin(u))=cos(u)	prove\:\tan(u)(\csc(u)-\sin(u))=\cos(u)
verificar 1-2sin^2(x)+sin^4(x)=cos^4(x)	prove\:1-2\sin^{2}(x)+\sin^{4}(x)=\cos^{4}(x)
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)
verificar 6cos^2(x)-3=3-6sin^2(x)	prove\:6\cos^{2}(x)-3=3-6\sin^{2}(x)
verificar sin(x)tan(x)+cos(-x)=sec(x)	prove\:\sin(x)\tan(x)+\cos(-x)=\sec(x)
verificar (1-cos(B))(1+cos(B))= 1/(csc^2(B))	prove\:(1-\cos(B))(1+\cos(B))=\frac{1}{\csc^{2}(B)}
verificar cot(θ)-tan(θ)=2cot(2θ)	prove\:\cot(θ)-\tan(θ)=2\cot(2θ)
verificar sin^2(u)=(1-cos(2u))/2	prove\:\sin^{2}(u)=\frac{1-\cos(2u)}{2}
verificar cot(2x)=(sec(x)+csc(x))/(2sin(x)-2cos(x))	prove\:\cot(2x)=\frac{\sec(x)+\csc(x)}{2\sin(x)-2\cos(x)}
verificar cos(-x)=-cos(x)	prove\:\cos(-x)=-\cos(x)
verificar sin^2(x)cos^2(x)= 1/4 sin^2(2x)	prove\:\sin^{2}(x)\cos^{2}(x)=\frac{1}{4}\sin^{2}(2x)
verificar cot^2(a)=cos^2(a)+((cot(a))(cos(a)))^2	prove\:\cot^{2}(a)=\cos^{2}(a)+((\cot(a))(\cos(a)))^{2}
verificar (1-sin^2(t))(1+tan^2(t))=1	prove\:(1-\sin^{2}(t))(1+\tan^{2}(t))=1
verificar 1-cosh^2(x)=-sinh^2(x)	prove\:1-\cosh^{2}(x)=-\sinh^{2}(x)
verificar cot^2(θ)+1=csc^2(θ)	prove\:\cot^{2}(θ)+1=\csc^{2}(θ)
verificar 2cos(θ)tan(θ)csc(θ)=2	prove\:2\cos(θ)\tan(θ)\csc(θ)=2
verificar ((cos^2(x)+4cos(x)+4))/((cos(x)+2))=((2sec(x)+1))/(sec(x))	prove\:\frac{(\cos^{2}(x)+4\cos(x)+4)}{(\cos(x)+2)}=\frac{(2\sec(x)+1)}{\sec(x)}
verificar 5cos^2(x)-5sin^2(x)=10cos^2(x)-5	prove\:5\cos^{2}(x)-5\sin^{2}(x)=10\cos^{2}(x)-5
verificar tan(x)=((1-cos(2x)))/((sin(2x)))	prove\:\tan(x)=\frac{(1-\cos(2x))}{(\sin(2x))}
verificar cot(pi-θ)=-cot(θ)	prove\:\cot(π-θ)=-\cot(θ)
verificar sin(x+2pi)=sin(x)	prove\:\sin(x+2π)=\sin(x)
verificar (cos(3a)cos(2a))/(sin(3a)sin(2a))=(cot(2a))/(tan(3a))	prove\:\frac{\cos(3a)\cos(2a)}{\sin(3a)\sin(2a)}=\frac{\cot(2a)}{\tan(3a)}
verificar 1/(cos^2(θ))=tan^2(θ)+1	prove\:\frac{1}{\cos^{2}(θ)}=\tan^{2}(θ)+1
verificar 1/2 (cot(θ)-tan(θ))=cot(2θ)	prove\:\frac{1}{2}(\cot(θ)-\tan(θ))=\cot(2θ)
verificar sin^2(x/2)=(sec(x)-1)/(2sec(x))	prove\:\sin^{2}(\frac{x}{2})=\frac{\sec(x)-1}{2\sec(x)}
verificar cos(x)-cos(x)=0	prove\:\cos(x)-\cos(x)=0
verificar (csc^2(θ)-2)/(csc^2(θ))=cos(2θ)	prove\:\frac{\csc^{2}(θ)-2}{\csc^{2}(θ)}=\cos(2θ)
verificar sin(-x)cos(pi/2-x)=(cos(2x)-1)/2	prove\:\sin(-x)\cos(\frac{π}{2}-x)=\frac{\cos(2x)-1}{2}
verificar cos(b)+sin(b)tan(b)=sec(b)	prove\:\cos(b)+\sin(b)\tan(b)=\sec(b)
verificar 2sin(2θ)(1-2sin^2(θ))=sin(4θ)	prove\:2\sin(2θ)(1-2\sin^{2}(θ))=\sin(4θ)
verificar ((cos^2(x)))/(1-sin(x))=1+sin(x)	prove\:\frac{(\cos^{2}(x))}{1-\sin(x)}=1+\sin(x)
verificar sin(3x)=sin(x)(3-4sin^2(x))	prove\:\sin(3x)=\sin(x)(3-4\sin^{2}(x))
verificar 1+sec(θ)tan(θ)sin(θ)=sec^2(θ)	prove\:1+\sec(θ)\tan(θ)\sin(θ)=\sec^{2}(θ)
verificar cos^2(a)+sin^2(a)=1	prove\:\cos^{2}(a)+\sin^{2}(a)=1
verificar csc(x)sin(pi/2-x)=cot(x)	prove\:\csc(x)\sin(\frac{π}{2}-x)=\cot(x)
verificar cos(4θ)=2(cos(2θ))^2-1	prove\:\cos(4θ)=2(\cos(2θ))^{2}-1
verificar tan(2x)=(2sin(x)cos(x))/(2cos^2(x)-1)	prove\:\tan(2x)=\frac{2\sin(x)\cos(x)}{2\cos^{2}(x)-1}
verificar 1/(csc^2(x))+1/(sec^2(x))=1	prove\:\frac{1}{\csc^{2}(x)}+\frac{1}{\sec^{2}(x)}=1
verificar cot((5pi)/(12))=2-sqrt(3)	prove\:\cot(\frac{5π}{12})=2-\sqrt{3}
verificar cos(4x)=cos^2(2x)-sin^2(2x)	prove\:\cos(4x)=\cos^{2}(2x)-\sin^{2}(2x)
verificar (cos^3(t))/(cot^2(t))=sin^2(t)cos(t)	prove\:\frac{\cos^{3}(t)}{\cot^{2}(t)}=\sin^{2}(t)\cos(t)
verificar cos(a+b)cos(a-b)=cos^2(a)-cos^2(b)	prove\:\cos(a+b)\cos(a-b)=\cos^{2}(a)-\cos^{2}(b)
verificar tan(x)sin(2x)=2sin^2(x)	prove\:\tan(x)\sin(2x)=2\sin^{2}(x)
verificar cot(x)tan(x)-(sin^2(x)+cos^2(x))=0	prove\:\cot(x)\tan(x)-(\sin^{2}(x)+\cos^{2}(x))=0
verificar cos(x)sec(x)=tan(x)cot(x)	prove\:\cos(x)\sec(x)=\tan(x)\cot(x)
verificar (csc(x))/(1+cot^2(x))=sin(x)	prove\:\frac{\csc(x)}{1+\cot^{2}(x)}=\sin(x)
verificar csc(pi/2-x)cot(x)=csc(x)	prove\:\csc(\frac{π}{2}-x)\cot(x)=\csc(x)
verificar sec((3pi)/2-x)=-csc(x)	prove\:\sec(\frac{3π}{2}-x)=-\csc(x)
verificar cos(x)+sin(x)tan(x)= 1/(cos(x))	prove\:\cos(x)+\sin(x)\tan(x)=\frac{1}{\cos(x)}
verificar cos(2θ)=(csc^2(θ)-2)/(csc^2(θ))	prove\:\cos(2θ)=\frac{\csc^{2}(θ)-2}{\csc^{2}(θ)}
verificar sin(x)=-sin(-x)	prove\:\sin(x)=-\sin(-x)
verificar tan(x)+cot(x)=(csc(x))/(cos(x))	prove\:\tan(x)+\cot(x)=\frac{\csc(x)}{\cos(x)}
verificar sec(θ)-tan(θ)sin(θ)=cos(θ)	prove\:\sec(θ)-\tan(θ)\sin(θ)=\cos(θ)
verificar 4-8sin^2(x)=4cos(2x)	prove\:4-8\sin^{2}(x)=4\cos(2x)
verificar 4cos^3(θ)-3cos(θ)=cos(3θ)	prove\:4\cos^{3}(θ)-3\cos(θ)=\cos(3θ)

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