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Problemas populares de Trigonometría

verificar tan(11/12 pi)=tan(-pi/(12))	prove\:\tan(\frac{11}{12}π)=\tan(-\frac{π}{12})
verificar cot(B)sec(B)sin(B)=1	prove\:\cot(B)\sec(B)\sin(B)=1
verificar (cos(x)-tan(x))/(sin(x)-cot(x))=-1	prove\:\frac{\cos(x)-\tan(x)}{\sin(x)-\cot(x)}=-1
verificar 1-2sin^2(2A)=8cos^4(A)-8cos^2(A)+1	prove\:1-2\sin^{2}(2A)=8\cos^{4}(A)-8\cos^{2}(A)+1
verificar (1+cot(x))/(csc(x))=sin(x)cos(x)	prove\:\frac{1+\cot(x)}{\csc(x)}=\sin(x)\cos(x)
verificar sin^2(θ-α)=cos(θ)	prove\:\sin^{2}(θ-α)=\cos(θ)
verificar cos(2x)cos(2x)=cos^2(2x)	prove\:\cos(2x)\cos(2x)=\cos^{2}(2x)
verificar cos(pi)=-1	prove\:\cos(π)=-1
verificar cos^2(x)+cot^2(x)=cos^2(x)cot^2(x)	prove\:\cos^{2}(x)+\cot^{2}(x)=\cos^{2}(x)\cot^{2}(x)
verificar sec^2(x)sin^2(x)= 1/(cot^2(x))	prove\:\sec^{2}(x)\sin^{2}(x)=\frac{1}{\cot^{2}(x)}
verificar (csc(θ))/(1+tan(θ))=cot^2(θ)	prove\:\frac{\csc(θ)}{1+\tan(θ)}=\cot^{2}(θ)
verificar-(-1+sin^2(θ))/(sin^2(θ))=cot^2(θ)	prove\:-\frac{-1+\sin^{2}(θ)}{\sin^{2}(θ)}=\cot^{2}(θ)
verificar cos(2A+A)=-3cos(A)+4cos^3(A)	prove\:\cos(2A+A)=-3\cos(A)+4\cos^{3}(A)
verificar tan(x)cos^2(x)csc^2(x)=cot(x)	prove\:\tan(x)\cos^{2}(x)\csc^{2}(x)=\cot(x)
verificar (sin^2(x)+cos^2(x))^3=1^3	prove\:(\sin^{2}(x)+\cos^{2}(x))^{3}=1^{3}
verificar cos(-x)*cot(x)+sin(x)=csc(x)	prove\:\cos(-x)\cdot\:\cot(x)+\sin(x)=\csc(x)
verificar 0/(sin(θ))= 1/(sin(θ))+sqrt(3)	prove\:\frac{0}{\sin(θ)}=\frac{1}{\sin(θ)}+\sqrt{3}
verificar cos^2(x/2)= 1/2+1/2 cos(x)	prove\:\cos^{2}(\frac{x}{2})=\frac{1}{2}+\frac{1}{2}\cos(x)
verificar 2sin(x)-cot(x)=-cot(x)*2cot(x)	prove\:2\sin(x)-\cot(x)=-\cot(x)\cdot\:2\cot(x)
verificar 4cos^3(a)-3cos(a)=cos(3a)	prove\:4\cos^{3}(a)-3\cos(a)=\cos(3a)
verificar sin^2(θ)+(1/2)^2=1	prove\:\sin^{2}(θ)+(\frac{1}{2})^{2}=1
verificar (csc^2(x)-1)sin(x)=cos^2(csc(x))	prove\:(\csc^{2}(x)-1)\sin(x)=\cos^{2}(\csc(x))
verificar sin(θ)(cot(θ)+tan(θ))=tan(θ)	prove\:\sin(θ)(\cot(θ)+\tan(θ))=\tan(θ)
verificar-csc^2(x)=(sec(x))/(2sin(x))	prove\:-\csc^{2}(x)=\frac{\sec(x)}{2\sin(x)}
verificar (sec(x)cos(x))/(cot(x))=tan(x)	prove\:\frac{\sec(x)\cos(x)}{\cot(x)}=\tan(x)
verificar 2sin^2((9θ)/2)=1-cos(9θ)	prove\:2\sin^{2}(\frac{9θ}{2})=1-\cos(9θ)
verificar cos(x)cos(x)=cos^2(x)	prove\:\cos(x)\cos(x)=\cos^{2}(x)
verificar sqrt(81-9(3sin(x))^2)=-1	prove\:\sqrt{81-9(3\sin(x))^{2}}=-1
verificar ((sin(2x))/(1-cos(2x)))=cot(x)	prove\:(\frac{\sin(2x)}{1-\cos(2x)})=\cot(x)
verificar csc(x)+1= 2/(sin(x))	prove\:\csc(x)+1=\frac{2}{\sin(x)}
verificar csc(x)=-5/4	prove\:\csc(x)=-\frac{5}{4}
verificar cos(2x)+cos^2(x)=1	prove\:\cos(2x)+\cos^{2}(x)=1
verificar 1/(cos(x))=arccos(x)	prove\:\frac{1}{\cos(x)}=\arccos(x)
verificar tan^2(x)sec(x)=cot^2(x)csc(x)	prove\:\tan^{2}(x)\sec(x)=\cot^{2}(x)\csc(x)
verificar (sec^2(x)-1)csc(x)=tan^2(x)csc(x)	prove\:(\sec^{2}(x)-1)\csc(x)=\tan^{2}(x)\csc(x)
verificar 1-sec(x)=((cos(x)-1))/(cos(x))	prove\:1-\sec(x)=\frac{(\cos(x)-1)}{\cos(x)}
verificar cos^4(t)-sin^4(t)=1-2cos^2(t)	prove\:\cos^{4}(t)-\sin^{4}(t)=1-2\cos^{2}(t)
verificar (1+sec(θ))(1-cos(θ))=sec(θ)-cos(θ)	prove\:(1+\sec(θ))(1-\cos(θ))=\sec(θ)-\cos(θ)
verificar sin^3(x)=(1-cos^2(x))sin(x)	prove\:\sin^{3}(x)=(1-\cos^{2}(x))\sin(x)
verificar cos^2(x)cot^2(x)=cos^2(x)+cot^2(x)	prove\:\cos^{2}(x)\cot^{2}(x)=\cos^{2}(x)+\cot^{2}(x)
verificar 6cos^2(x)-6sin^2(x)=6-12sin^2(x)	prove\:6\cos^{2}(x)-6\sin^{2}(x)=6-12\sin^{2}(x)
verificar sin(x-3.14)=-sin(x)	prove\:\sin(x-3.14)=-\sin(x)
verificar cos^8(x)=sin^5(x)cos^3(x)	prove\:\cos^{8}(x)=\sin^{5}(x)\cos^{3}(x)
verificar 2sec(2x)=tan(pi/4+x)+tan(pi/4-x)	prove\:2\sec(2x)=\tan(\frac{π}{4}+x)+\tan(\frac{π}{4}-x)
verificar sin(x)-csc(x)=-(cos(x))(cot(x))	prove\:\sin(x)-\csc(x)=-(\cos(x))(\cot(x))
verificar tan(θ)cot(θ)=cos^2(θ)+sin^2(θ)	prove\:\tan(θ)\cot(θ)=\cos^{2}(θ)+\sin^{2}(θ)
verificar cos(θ)=sin(3θ+62)	prove\:\cos(θ)=\sin(3θ+62)
verificar sin(pix)+sin(pi(10-x))=0	prove\:\sin(π\cdot\:x)+\sin(π\cdot\:(10-x))=0
verificar cot(2θ)= 1/2 (tan(θ)-cot(θ))	prove\:\cot(2θ)=\frac{1}{2}(\tan(θ)-\cot(θ))
verificar sin(4x)=(2)(sin(2x))(cos(2x))	prove\:\sin(4x)=(2)(\sin(2x))(\cos(2x))
verificar-cos^2(x)+1=sin^2(x)	prove\:-\cos^{2}(x)+1=\sin^{2}(x)
verificar sin(x)sin(x)=cos(x)	prove\:\sin(x)\sin(x)=\cos(x)
verificar (tan(x)+sin(x))/(tan(x))=1+cos(x)	prove\:\frac{\tan(x)+\sin(x)}{\tan(x)}=1+\cos(x)
verificar sin(x)=-cos(pi/2+x)	prove\:\sin(x)=-\cos(\frac{π}{2}+x)
verificar 1-((sin^2(θ)))/(1+cos(θ))=cos(θ)	prove\:1-\frac{(\sin^{2}(θ))}{1+\cos(θ)}=\cos(θ)
verificar 4sin^2(x)+2cos^2(x)=-2+4sin^2(x)	prove\:4\sin^{2}(x)+2\cos^{2}(x)=-2+4\sin^{2}(x)
verificar arctan(-4/3)=-arctan(4/3)	prove\:\arctan(-\frac{4}{3})=-\arctan(\frac{4}{3})
verificar (1-cos^2(x))/(sin(x)cos(x))=tan(x)	prove\:\frac{1-\cos^{2}(x)}{\sin(x)\cos(x)}=\tan(x)
verificar sin(x)cos(x)=csc(x)	prove\:\sin(x)\cos(x)=\csc(x)
verificar cos(pi+x)+cos(2pi-x)=0	prove\:\cos(π+x)+\cos(2π-x)=0
verificar tan(μ)sec(μ)cos(μ)=tan(μ)	prove\:\tan(μ)\sec(μ)\cos(μ)=\tan(μ)
verificar csc(x)-csc(x)cos^{(2)}(x)=sin(x)	prove\:\csc(x)-\csc(x)\cos^{(2)}(x)=\sin(x)
verificar (1+cos(θ))*tan(θ/2)=sin(θ)	prove\:(1+\cos(θ))\cdot\:\tan(\frac{θ}{2})=\sin(θ)
verificar csc(θ)-cot(θ)=1	prove\:\csc(θ)-\cot(θ)=1
verificar 5(sin^2(x)-1)=5cot^2(x)	prove\:5(\sin^{2}(x)-1)=5\cot^{2}(x)
verificar (sec^2(x))/(tan(x))=cot(x)+tan(x)	prove\:\frac{\sec^{2}(x)}{\tan(x)}=\cot(x)+\tan(x)
verificar cos(z)=sin(pi/2+z)	prove\:\cos(z)=\sin(\frac{π}{2}+z)
verificar sin^2(θ)(2+cot^2(θ))=1	prove\:\sin^{2}(θ)(2+\cot^{2}(θ))=1
verificar 5sin(x)*cos(x)=5(1-cos^2(x))cot(x)	prove\:5\sin(x)\cdot\:\cos(x)=5(1-\cos^{2}(x))\cot(x)
verificar-cos^2(2θ)=(1+cos(4θ))/8	prove\:-\cos^{2}(2θ)=\frac{1+\cos(4θ)}{8}
verificar tan^2(x)=2sin^2(x)-1	prove\:\tan^{2}(x)=2\sin^{2}(x)-1
verificar tan(-pi/2-θ)=cot(θ)	prove\:\tan(-\frac{π}{2}-θ)=\cot(θ)
verificar cos(2x)+tan(x)sin(2x)=1	prove\:\cos(2x)+\tan(x)\sin(2x)=1
verificar ((1+tan(θ)))/((1+cot(θ)))=tan(θ)	prove\:\frac{(1+\tan(θ))}{(1+\cot(θ))}=\tan(θ)
verificar 1/(sin^2(θ))=1-tan^2(θ)	prove\:\frac{1}{\sin^{2}(θ)}=1-\tan^{2}(θ)
verificar 1/((sec(θ))^2)+1/((csc(θ))^2)=1	prove\:\frac{1}{(\sec(θ))^{2}}+\frac{1}{(\csc(θ))^{2}}=1
verificar sin^2(a/2)=(1-cos(a))/2	prove\:\sin^{2}(\frac{a}{2})=\frac{1-\cos(a)}{2}
verificar tan(x)-tan(x)sin(x)=cos(x)sin(x)	prove\:\tan(x)-\tan(x)\sin(x)=\cos(x)\sin(x)
verificar cot(x)+tan(x)=sec(csc(x))	prove\:\cot(x)+\tan(x)=\sec(\csc(x))
verificar cos(1/3 pi)=cos(-1/3 pi)	prove\:\cos(\frac{1}{3}π)=\cos(-\frac{1}{3}π)
verificar 7sec(θ)=-9.2	prove\:7\sec(θ)=-9.2
verificar (cot(x)+tan(x))cos(x)=csc(x)	prove\:(\cot(x)+\tan(x))\cos(x)=\csc(x)
verificar cos(-(5pi)/4)=cos((3pi)/4)	prove\:\cos(-\frac{5π}{4})=\cos(\frac{3π}{4})
verificar sqrt(cos^2(2x)+1+sin(2))=2	prove\:\sqrt{\cos^{2}(2x)+1+\sin(2)}=2
verificar (cos(k)-sec(k))^2=tan^2(-sin^2(k))	prove\:(\cos(k)-\sec(k))^{2}=\tan^{2}(-\sin^{2}(k))
verificar sin(x)=tan^2(x)cos^2(x)	prove\:\sin(x)=\tan^{2}(x)\cos^{2}(x)
verificar sin(2x+x)=3sin(x)-4sin^3(x)	prove\:\sin(2x+x)=3\sin(x)-4\sin^{3}(x)
verificar sin(3x)=2sin((3x)/2)cos((3x)/2)	prove\:\sin(3x)=2\cdot\:\sin(\frac{3x}{2})\cdot\:\cos(\frac{3x}{2})
verificar (sin(9x)-sin(3x))/(cos(9x)-cos(3x))=-(cos(6x))/(sin(6x))	prove\:\frac{\sin(9x)-\sin(3x)}{\cos(9x)-\cos(3x)}=-\frac{\cos(6x)}{\sin(6x)}
verificar (sec(a)-tan(a))(csc(a)+1)=cot(a)	prove\:(\sec(a)-\tan(a))(\csc(a)+1)=\cot(a)
verificar-cos(x)sin^2(x)=-cos(x)(sin(x))^2	prove\:-\cos(x)\sin^{2}(x)=-\cos(x)(\sin(x))^{2}
verificar (cot(x)+tan(x))^2=sec^2(x)csc^2(x)	prove\:(\cot(x)+\tan(x))^{2}=\sec^{2}(x)\csc^{2}(x)
verificar 6sin((5pi)/6)=2+2sin((5pi)/6)	prove\:6\sin(\frac{5π}{6})=2+2\sin(\frac{5π}{6})
verificar tan(2x)=-2sin(x)	prove\:\tan(2x)=-2\sin(x)
verificar 0/(sin(x)cos(x))=0	prove\:\frac{0}{\sin(x)\cos(x)}=0
verificar (sin(x))/(1-cos(x))=1	prove\:\frac{\sin(x)}{1-\cos(x)}=1
verificar cos((piθ)/2)=-0.25	prove\:\cos(\frac{πθ}{2})=-0.25
verificar cot(x)+1/(cot(x))=sin(x)cos(x)	prove\:\cot(x)+\frac{1}{\cot(x)}=\sin(x)\cos(x)
verificar (sin(2a))/(1-sin^2(a))=2tan(a)	prove\:\frac{\sin(2a)}{1-\sin^{2}(a)}=2\tan(a)
verificar cos(t)=sin(t+pi/2)	prove\:\cos(t)=\sin(t+\frac{π}{2})

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