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Problemas populares de Trigonometría

verificar csc(x)-sec(x)sin^2(x)=cos(x)	prove\:\csc(x)-\sec(x)\sin^{2}(x)=\cos(x)
verificar tan^2(x)+4=sec^2(x)+3	prove\:\tan^{2}(x)+4=\sec^{2}(x)+3
verificar ((1-csc(x)))/(cos(x)-cot(x))=sec(x)	prove\:\frac{(1-\csc(x))}{\cos(x)-\cot(x)}=\sec(x)
verificar sin(x-pi/2)=cos(x)	prove\:\sin(x-\frac{π}{2})=\cos(x)
verificar ((sec(x)-cos(x)))/(tan(x))=sin(x)	prove\:\frac{(\sec(x)-\cos(x))}{\tan(x)}=\sin(x)
verificar 2csc(2x)=sec^2(x)cot(x)	prove\:2\csc(2x)=\sec^{2}(x)\cot(x)
verificar cos^2(x)-cos^2(x)=0	prove\:\cos^{2}(x)-\cos^{2}(x)=0
verificar 2(sec(x)-tan(x))(csc(x)+1)=2cot(x)	prove\:2(\sec(x)-\tan(x))(\csc(x)+1)=2\cot(x)
verificar sec(x)sin(x)cot(x)=1	prove\:\sec(x)\sin(x)\cot(x)=1
verificar (cos^2(x))/(cot(x))=sin(x)cos(x)	prove\:\frac{\cos^{2}(x)}{\cot(x)}=\sin(x)\cos(x)
verificar cos^2(α)sec^2(α)=1	prove\:\cos^{2}(α)\sec^{2}(α)=1
verificar 2sin(x)cos(x)+4cos(2x)=1	prove\:2\sin(x)\cos(x)+4\cos(2x)=1
verificar 3-6sin^2(x)=3cos(2x)	prove\:3-6\sin^{2}(x)=3\cos(2x)
verificar 1+cos(2x)=3sin(x)	prove\:1+\cos(2x)=3\sin(x)
verificar sin^2(2θ)=(1-cos(4θ))/2	prove\:\sin^{2}(2θ)=\frac{1-\cos(4θ)}{2}
verificar (csc(a))/(1+cot^2(a))=sin(a)	prove\:\frac{\csc(a)}{1+\cot^{2}(a)}=\sin(a)
verificar 1/(tan(x))=arctan(x)	prove\:\frac{1}{\tan(x)}=\arctan(x)
verificar 1+cos^2(x)=2cos^2(x)+sin^2(x)	prove\:1+\cos^{2}(x)=2\cos^{2}(x)+\sin^{2}(x)
verificar sec(-x)= 1/(cos(x))	prove\:\sec(-x)=\frac{1}{\cos(x)}
verificar csc(x)=2	prove\:\csc(x)=2
verificar sin(x)csc^2(x)= 1/(sin(x))	prove\:\sin(x)\csc^{2}(x)=\frac{1}{\sin(x)}
verificar (cos(2θ))/(cos^2(θ))=1-tan^2(θ)	prove\:\frac{\cos(2θ)}{\cos^{2}(θ)}=1-\tan^{2}(θ)
verificar ((sec(θ)-tan(θ))^2+1)/(csc(θ)(sec(θ)-tan(θ)))=2tan(θ)	prove\:\frac{(\sec(θ)-\tan(θ))^{2}+1}{\csc(θ)(\sec(θ)-\tan(θ))}=2\tan(θ)
verificar 2csc(2x)=sec(x)csc(x)	prove\:2\csc(2x)=\sec(x)\csc(x)
verificar (tan(θ+1))=sec(θ)	prove\:(\tan(θ+1))=\sec(θ)
verificar tan(x/2)=(sin(x))/(cos(x)+1)	prove\:\tan(\frac{x}{2})=\frac{\sin(x)}{\cos(x)+1}
verificar (sin(x)csc(x))/(cos(x))=sec(x)	prove\:\frac{\sin(x)\csc(x)}{\cos(x)}=\sec(x)
verificar tan(x)+sec(x)=1	prove\:\tan(x)+\sec(x)=1
verificar-sinh^2(x)+cosh^2(x)=1	prove\:-\sinh^{2}(x)+\cosh^{2}(x)=1
verificar sin^2(x)+cos^2(x)-1=0	prove\:\sin^{2}(x)+\cos^{2}(x)-1=0
verificar sec(x)sin(pi/2-x)=1	prove\:\sec(x)\sin(\frac{π}{2}-x)=1
verificar csc(x)tan^2(x)=(sin(x))/(cos^2(x))	prove\:\csc(x)\tan^{2}(x)=\frac{\sin(x)}{\cos^{2}(x)}
verificar (tan(x))/(sin(x))= 1/(cos(x))	prove\:\frac{\tan(x)}{\sin(x)}=\frac{1}{\cos(x)}
verificar cos^4(x)-sin^4(x)=2sin^2(x)-1	prove\:\cos^{4}(x)-\sin^{4}(x)=2\sin^{2}(x)-1
verificar 2sin^2(x)+cos^2(x)=1+sin^2(x)	prove\:2\sin^{2}(x)+\cos^{2}(x)=1+\sin^{2}(x)
verificar 1/(cos^2(x)2tan(x))=csc(2x)	prove\:\frac{1}{\cos^{2}(x)2\tan(x)}=\csc(2x)
verificar (1-cos(θ))(1+sec(θ))=sin(θ)tan(θ)	prove\:(1-\cos(θ))(1+\sec(θ))=\sin(θ)\tan(θ)
verificar tan(y)-(sec^2(y))/(tan(y))=-cot(y)	prove\:\tan(y)-\frac{\sec^{2}(y)}{\tan(y)}=-\cot(y)
verificar (csc(x)-cot(x))(sec(x)1)=tan(x)	prove\:(\csc(x)-\cot(x))(\sec(x)1)=\tan(x)
verificar-(cos^2(x))/(sin(x))=-cos(x)cot(x)	prove\:-\frac{\cos^{2}(x)}{\sin(x)}=-\cos(x)\cot(x)
verificar tan(2t)=2sin(t)cos(t)sec(2t)	prove\:\tan(2t)=2\sin(t)\cos(t)\sec(2t)
verificar-sec(2x)=(1+cot^2(x))/(1-cot^2(x))	prove\:-\sec(2x)=\frac{1+\cot^{2}(x)}{1-\cot^{2}(x)}
verificar tan^3(x)-tan(x)sec^2(x)=tan(-x)	prove\:\tan^{3}(x)-\tan(x)\sec^{2}(x)=\tan(-x)
verificar sec(pi-x)=-sec(x)	prove\:\sec(π-x)=-\sec(x)
verificar sin(-x)-cos(-x)=-(sin(x)+cos(x))	prove\:\sin(-x)-\cos(-x)=-(\sin(x)+\cos(x))
verificar (csc^2(θ)-1)/(cos(θ))=cot(θ)csc(θ)	prove\:\frac{\csc^{2}(θ)-1}{\cos(θ)}=\cot(θ)\csc(θ)
verificar sec(a)-cos(a)csc(a)-sin(a)=tan(3a)	prove\:\sec(a)-\cos(a)\csc(a)-\sin(a)=\tan(3a)
verificar cos^2(x)=sin(x)	prove\:\cos^{2}(x)=\sin(x)
verificar 1-(cos^2(u))/(1-sin(u))=-sin(u)	prove\:1-\frac{\cos^{2}(u)}{1-\sin(u)}=-\sin(u)
verificar tan(θ)(cot(θ)cos(θ)+sin(θ))=sec(θ)	prove\:\tan(θ)(\cot(θ)\cos(θ)+\sin(θ))=\sec(θ)
verificar 2(1-sin^2(x))=cos(2x)+1	prove\:2(1-\sin^{2}(x))=\cos(2x)+1
verificar sin^2(t)=(1-cos(2t))/2	prove\:\sin^{2}(t)=\frac{1-\cos(2t)}{2}
verificar sin(y)sec(y)=tan(y)	prove\:\sin(y)\sec(y)=\tan(y)
verificar 2-cos^2(x)=sin^2(x)	prove\:2-\cos^{2}(x)=\sin^{2}(x)
verificar 4sin(7pi-x)=4sin(x)	prove\:4\sin(7π-x)=4\sin(x)
verificar tan(15)=tan(45-30)	prove\:\tan(15^{\circ\:})=\tan(45^{\circ\:}-30^{\circ\:})
verificar cos(2x+pi/3)+2=2cos^2(x+pi/6)	prove\:\cos(2x+\frac{π}{3})+2=2\cos^{2}(x+\frac{π}{6})
verificar 2csc(2u)=tan(u)+cot(u)	prove\:2\csc(2u)=\tan(u)+\cot(u)
verificar sec(x)sin(2x)=2sin(x)	prove\:\sec(x)\sin(2x)=2\sin(x)
verificar sec(x)cot(x)-cot(x)cos(x)=sin(x)	prove\:\sec(x)\cot(x)-\cot(x)\cos(x)=\sin(x)
verificar cos(x)*cot(x)=csc(x)-sin(x)	prove\:\cos(x)\cdot\:\cot(x)=\csc(x)-\sin(x)
verificar cos(x+270)=sin(x)	prove\:\cos(x+270^{\circ\:})=\sin(x)
verificar cos(u)sec(u)-sin^2(u)=cos^2(u)	prove\:\cos(u)\sec(u)-\sin^{2}(u)=\cos^{2}(u)
verificar cos^4(x)=cos^2(x)cos^2(x)	prove\:\cos^{4}(x)=\cos^{2}(x)\cos^{2}(x)
verificar cot(x)-2cot(2x)=tan(x)	prove\:\cot(x)-2\cot(2x)=\tan(x)
verificar sin(x)=sqrt(3)sin(x/2)	prove\:\sin(x)=\sqrt{3}\sin(\frac{x}{2})
verificar sin(θ)cos(θ)sec(θ)csc(θ)=1	prove\:\sin(θ)\cos(θ)\sec(θ)\csc(θ)=1
verificar sin(pi/2-0)=cos(0)	prove\:\sin(\frac{π}{2}-0)=\cos(0)
verificar sin(3x)=sin(3-4sin^2(x))	prove\:\sin(3x)=\sin(3-4\sin^{2}(x))
verificar (tan^2(θ))/(sec(θ)+1)=sec(θ)-1	prove\:\frac{\tan^{2}(θ)}{\sec(θ)+1}=\sec(θ)-1
verificar 1+1/(cos(x))=(tan^2(x))/(sec(x)-1)	prove\:1+\frac{1}{\cos(x)}=\frac{\tan^{2}(x)}{\sec(x)-1}
verificar cot(x)-1=(csc(x)-sec(x))/(sec(x))	prove\:\cot(x)-1=\frac{\csc(x)-\sec(x)}{\sec(x)}
verificar tan(θ)=2	prove\:\tan(θ)=2
verificar sec(x)=sec(-x)	prove\:\sec(x)=\sec(-x)
verificar cot^2(θ)=cos^2(θ)+(cot(θ)cos(θ))^2	prove\:\cot^{2}(θ)=\cos^{2}(θ)+(\cot(θ)\cos(θ))^{2}
verificar csc^2(θ)-1=cot^2(θ)	prove\:\csc^{2}(θ)-1=\cot^{2}(θ)
verificar tan(u)+cot(u)=sec(u)csc(u)	prove\:\tan(u)+\cot(u)=\sec(u)\csc(u)
verificar ((cot(a)))/((csc(a)))=cos(a)	prove\:\frac{(\cot(a))}{(\csc(a))}=\cos(a)
verificar cos(pi/(12))=(sqrt(2+\sqrt{3)})/2	prove\:\cos(\frac{π}{12})=\frac{\sqrt{2+\sqrt{3}}}{2}
verificar tan(θ)=sqrt(tan(θ)+2)	prove\:\tan(θ)=\sqrt{\tan(θ)+2}
verificar tan(2u)=(2tan(u))/(1-tan^2(u))	prove\:\tan(2u)=\frac{2\tan(u)}{1-\tan^{2}(u)}
verificar (3sec(θ)-3)/(1-cos(θ))=3sec(θ)	prove\:\frac{3\sec(θ)-3}{1-\cos(θ)}=3\sec(θ)
verificar cot(pi/2-θ)=tan(θ)	prove\:\cot(\frac{π}{2}-θ)=\tan(θ)
verificar cos(pi/2-a)=sin(a)	prove\:\cos(\frac{π}{2}-a)=\sin(a)
verificar (1-cos^2(x))(csc(x))=sin(x)	prove\:(1-\cos^{2}(x))(\csc(x))=\sin(x)
verificar (sin(x+y))/(sin(x)cos(y))=1+cot(x)tan(y)	prove\:\frac{\sin(x+y)}{\sin(x)\cos(y)}=1+\cot(x)\tan(y)
verificar (sin(x)+cos(x))^2-sin(2x)=1	prove\:(\sin(x)+\cos(x))^{2}-\sin(2x)=1
verificar sin^2(2x)= 1/2-1/2 cos(4x)	prove\:\sin^{2}(2x)=\frac{1}{2}-\frac{1}{2}\cos(4x)
verificar 1/(1+tan(x)tan(2x))=cos(2x)	prove\:\frac{1}{1+\tan(x)\tan(2x)}=\cos(2x)
verificar sin(a/2)= 1/2 sin(a)	prove\:\sin(\frac{a}{2})=\frac{1}{2}\sin(a)
verificar (1+csc(x))(1-sin(x))=cot(x)cos(x)	prove\:(1+\csc(x))(1-\sin(x))=\cot(x)\cos(x)
verificar (sin(5x)-sin(x))/(cos(5x)-cos(x))=-cot(3x)	prove\:\frac{\sin(5x)-\sin(x)}{\cos(5x)-\cos(x)}=-\cot(3x)
verificar tan^2(α)=(sin^2(α))/(1-sin^2(α))	prove\:\tan^{2}(α)=\frac{\sin^{2}(α)}{1-\sin^{2}(α)}
verificar ((1-cot^2(x)))/(1+cot^2(x))+1=2sin^2(x)	prove\:\frac{(1-\cot^{2}(x))}{1+\cot^{2}(x)}+1=2\sin^{2}(x)
verificar tan(x)sec(x)(csc(x)-sin(x))=1	prove\:\tan(x)\sec(x)(\csc(x)-\sin(x))=1
verificar csc(x)cos(x)cot(x)=sin(x)	prove\:\csc(x)\cos(x)\cot(x)=\sin(x)
verificar 2cos(x)+2sin(x)tan(x)=2sec(x)	prove\:2\cos(x)+2\sin(x)\tan(x)=2\sec(x)
verificar sin^4(x)+cos^4(x)=1	prove\:\sin^{4}(x)+\cos^{4}(x)=1
verificar arcsec(x)= 1/(sec(x))	prove\:\arcsec(x)=\frac{1}{\sec(x)}
verificar cos(4x)cos(2x)=cos^2(3x)-cos^2(x)	prove\:\cos(4x)\cos(2x)=\cos^{2}(3x)-\cos^{2}(x)

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