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Problemas populares de Trigonometría

verificar tan^2(a)=(tan(a))^2	prove\:\tan^{2}(a)=(\tan(a))^{2}
verificar (1-cos(θ^2))(1+cot(θ^2))=1	prove\:(1-\cos(θ^{2}))(1+\cot(θ^{2}))=1
verificar cos(2x)=(2-sec^2(x))/(sec^2(x))	prove\:\cos(2x)=\frac{2-\sec^{2}(x)}{\sec^{2}(x)}
verificar cot(y)=(sin(2y))/(1-cos(2y))	prove\:\cot(y)=\frac{\sin(2y)}{1-\cos(2y)}
verificar 1+1/(tan^2(α))= 1/(sin^2(α))	prove\:1+\frac{1}{\tan^{2}(α)}=\frac{1}{\sin^{2}(α)}
verificar tan(x)+sec(x)=(sin(x)+1)/(cos(x))	prove\:\tan(x)+\sec(x)=\frac{\sin(x)+1}{\cos(x)}
verificar sin(x)-tan(x)= 1/(sec(x)tan(x))	prove\:\sin(x)-\tan(x)=\frac{1}{\sec(x)\tan(x)}
verificar (sin(t)cos(t))/(tan(t))=cos^2(t)	prove\:\frac{\sin(t)\cos(t)}{\tan(t)}=\cos^{2}(t)
verificar (tan(x))/(1-cot(x))+(cot(x))/(1-tan(x))=1+sec(x)sin(x)	prove\:\frac{\tan(x)}{1-\cot(x)}+\frac{\cot(x)}{1-\tan(x)}=1+\sec(x)\sin(x)
verificar sec(θ)(sec(θ)-cos(θ))=tan^2(θ)	prove\:\sec(θ)(\sec(θ)-\cos(θ))=\tan^{2}(θ)
verificar cot^2(θ)=(cos^2(θ))/(sin^2(θ))	prove\:\cot^{2}(θ)=\frac{\cos^{2}(θ)}{\sin^{2}(θ)}
verificar cos(pi)=cos(-pi)	prove\:\cos(π)=\cos(-π)
verificar 2(1+sin^2(x))=cos(2x)+1	prove\:2(1+\sin^{2}(x))=\cos(2x)+1
verificar sec^2(θ)-1=(tan(θ))/(cot(θ))	prove\:\sec^{2}(θ)-1=\frac{\tan(θ)}{\cot(θ)}
verificar cot(x)=(sin(2x))/(1-cos(x^2))	prove\:\cot(x)=\frac{\sin(2x)}{1-\cos(x^{2})}
verificar cos(2x)=cos(x)cos(x)-sin(x)sin(x)	prove\:\cos(2x)=\cos(x)\cos(x)-\sin(x)\sin(x)
verificar (8/6)^2+1=(10/6)^2	prove\:(\frac{8}{6})^{2}+1=(\frac{10}{6})^{2}
verificar sec^4(θ)-tan^4(θ)=2tan^2(θ)+1	prove\:\sec^{4}(θ)-\tan^{4}(θ)=2\tan^{2}(θ)+1
verificar tan^2(x)(1+cot^2(x))=sec^2(x)	prove\:\tan^{2}(x)(1+\cot^{2}(x))=\sec^{2}(x)
verificar (1-sin(x))/(cos(x))=1-tan(x)	prove\:\frac{1-\sin(x)}{\cos(x)}=1-\tan(x)
verificar 1-cos^2(x)-cos^2(x)=1-2cos^2(x)	prove\:1-\cos^{2}(x)-\cos^{2}(x)=1-2\cos^{2}(x)
verificar ((1+cot^2(x)))/(sec^2(x))=cot^2(x)	prove\:\frac{(1+\cot^{2}(x))}{\sec^{2}(x)}=\cot^{2}(x)
verificar cot(s)+tan(s)=sec(s)csc(s)	prove\:\cot(s)+\tan(s)=\sec(s)\csc(s)
verificar cos(-pi/4)=sin(pi/4)	prove\:\cos(-\frac{π}{4})=\sin(\frac{π}{4})
verificar sin(u)cos(u)= 1/2 sin(2u)	prove\:\sin(u)\cos(u)=\frac{1}{2}\sin(2u)
verificar (cot(x)-1)^2=csc^2(x)-2cot(x)	prove\:(\cot(x)-1)^{2}=\csc^{2}(x)-2\cot(x)
verificar cot(2θ)=((cot^2(θ)-1))/(2cot(θ))	prove\:\cot(2θ)=\frac{(\cot^{2}(θ)-1)}{2\cot(θ)}
verificar cos^2(θ)=(1/(sec^2(θ)))	prove\:\cos^{2}(θ)=(\frac{1}{\sec^{2}(θ)})
verificar 1/(tan(θ))=cot(θ)	prove\:\frac{1}{\tan(θ)}=\cot(θ)
verificar tan(2x)cos(2x)=sin(2x)	prove\:\tan(2x)\cos(2x)=\sin(2x)
verificar tan(x)=2sin(x)	prove\:\tan(x)=2\sin(x)
verificar (1-sin^4(a))/(cos^2(a))=2-cos^2(a)	prove\:\frac{1-\sin^{4}(a)}{\cos^{2}(a)}=2-\cos^{2}(a)
verificar tan^2(x)=(sec(x)+1)(sec(x)-1)	prove\:\tan^{2}(x)=(\sec(x)+1)(\sec(x)-1)
verificar cot(θ)sin(θ)=csc(θ)	prove\:\cot(θ)\sin(θ)=\csc(θ)
verificar (sin(2x)+sin(4x))/(cos(2x)+cos(4x))=tan(3x)	prove\:\frac{\sin(2x)+\sin(4x)}{\cos(2x)+\cos(4x)}=\tan(3x)
verificar sec(A)csc(A)=cos(A)tan(A)	prove\:\sec(A)\csc(A)=\cos(A)\tan(A)
verificar 1/(tan(b))+tan(b)=(sec^2(b))/(tan(b))	prove\:\frac{1}{\tan(b)}+\tan(b)=\frac{\sec^{2}(b)}{\tan(b)}
verificar cos^2(x)-sin^2(x)=tan^2(x)sin^2(x)	prove\:\cos^{2}(x)-\sin^{2}(x)=\tan^{2}(x)\sin^{2}(x)
verificar sin(2a)=2sin(a)	prove\:\sin(2a)=2\sin(a)
verificar cos^3(x)=(cos(x))^3	prove\:\cos^{3}(x)=(\cos(x))^{3}
verificar 1+(cot(A))^2=(csc(A))^2	prove\:1+(\cot(A))^{2}=(\csc(A))^{2}
verificar cos(b)(1+tan(b))^2=sec(b)+2sin(b)	prove\:\cos(b)(1+\tan(b))^{2}=\sec(b)+2\sin(b)
verificar 2cos(x)-sin^2(x)+2=0	prove\:2\cos(x)-\sin^{2}(x)+2=0
verificar csc^2(x)-csc(x)+9=11	prove\:\csc^{2}(x)-\csc(x)+9=11
verificar sec^2(θ)-1= 1/(cot^2(θ))	prove\:\sec^{2}(θ)-1=\frac{1}{\cot^{2}(θ)}
verificar 1/(cos(x)-cot(x))-(sec(x))/(sin(x)-1)=sec(x)	prove\:\frac{1}{\cos(x)-\cot(x)}-\frac{\sec(x)}{\sin(x)-1}=\sec(x)
verificar sin(x/2)=sqrt((1+sin(x))/2)	prove\:\sin(\frac{x}{2})=\sqrt{\frac{1+\sin(x)}{2}}
verificar (sec(θ)+csc(θ))/(1+tan(θ))=csc(θ)	prove\:\frac{\sec(θ)+\csc(θ)}{1+\tan(θ)}=\csc(θ)
verificar (cot(a)+tan(a))cos(a)=csc(a)	prove\:(\cot(a)+\tan(a))\cos(a)=\csc(a)
verificar (sin^2(x)-1)=-cos^2(x)	prove\:(\sin^{2}(x)-1)=-\cos^{2}(x)
verificar cos(-(xpi)/3)=cos((xpi)/3)	prove\:\cos(-\frac{xπ}{3})=\cos(\frac{xπ}{3})
verificar 1+sin(x)=cos(x)	prove\:1+\sin(x)=\cos(x)
verificar sin(2y)=(2tan(y))/(1+tan^2(y))	prove\:\sin(2y)=\frac{2\tan(y)}{1+\tan^{2}(y)}
verificar sec^2(β)+sec^2(β)= 2/(cos^2(β))	prove\:\sec^{2}(β)+\sec^{2}(β)=\frac{2}{\cos^{2}(β)}
verificar 3csc(x)-cot(x)=(3-cos(x))/(sin(x))	prove\:3\csc(x)-\cot(x)=\frac{3-\cos(x)}{\sin(x)}
verificar 1/(1-sin(θ))=sec^2(θ)+sec(θ)tan(θ)	prove\:\frac{1}{1-\sin(θ)}=\sec^{2}(θ)+\sec(θ)\tan(θ)
verificar 1/(tan^2(θ))-cos(θ)=cos^2(θ)	prove\:\frac{1}{\tan^{2}(θ)}-\cos(θ)=\cos^{2}(θ)
verificar 2sin(x)=tan(x)	prove\:2\sin(x)=\tan(x)
verificar 1sin(t)+(-1)cos(t-pi/2)=0	prove\:1\cdot\:\sin(t)+(-1)\cdot\:\cos(t-\frac{π}{2})=0
verificar (cot(x))/(sec(x)-tan(x))=csc(x)+1	prove\:\frac{\cot(x)}{\sec(x)-\tan(x)}=\csc(x)+1
verificar csc(x)-cot(x)= 1/((csc(x)+cot(x)))	prove\:\csc(x)-\cot(x)=\frac{1}{(\csc(x)+\cot(x))}
verificar (csc(x))/(cot(x))= 1/(cos(x))	prove\:\frac{\csc(x)}{\cot(x)}=\frac{1}{\cos(x)}
verificar (1+tan^2(θ))/(tan^2(θ))=csc^2(θ)	prove\:\frac{1+\tan^{2}(θ)}{\tan^{2}(θ)}=\csc^{2}(θ)
verificar (sin^2(x))/(tan(x))=sin(x)cos(x)	prove\:\frac{\sin^{2}(x)}{\tan(x)}=\sin(x)\cos(x)
verificar cot^4(x)+2cot^2(x)+1=csc^4(x)	prove\:\cot^{4}(x)+2\cot^{2}(x)+1=\csc^{4}(x)
verificar sin^2(β)+tan^2(β)+1= 2/(cos^2(β))	prove\:\sin^{2}(β)+\tan^{2}(β)+1=\frac{2}{\cos^{2}(β)}
verificar cot(x)-1=csc(x)(cos(x)-sin(x))	prove\:\cot(x)-1=\csc(x)(\cos(x)-\sin(x))
verificar sec(A)csc(A)=1	prove\:\sec(A)\csc(A)=1
verificar sin^2(x/2)-cos^2(x/2)=-cos(x)	prove\:\sin^{2}(\frac{x}{2})-\cos^{2}(\frac{x}{2})=-\cos(x)
verificar (tan^2(x))/(1+sec(x))=sec(x)-1	prove\:\frac{\tan^{2}(x)}{1+\sec(x)}=\sec(x)-1
verificar csc(x)=sin(x)	prove\:\csc(x)=\sin(x)
verificar-cos(x)=sin(x+pi/2)	prove\:-\cos(x)=\sin(x+\frac{π}{2})
verificar (cos(x)*sec(x))/(tan(x))=cot(x)	prove\:\frac{\cos(x)\cdot\:\sec(x)}{\tan(x)}=\cot(x)
verificar sqrt(81-9(3sin(x))^2)=12sec(x)	prove\:\sqrt{81-9(3\sin(x))^{2}}=12\sec(x)
verificar (1+cos(2x))/(1-cos(2x))=cot^2(x)	prove\:\frac{1+\cos(2x)}{1-\cos(2x)}=\cot^{2}(x)
verificar (1-cos(2x))/(cos^2(x))=2tan^2(x)	prove\:\frac{1-\cos(2x)}{\cos^{2}(x)}=2\tan^{2}(x)
verificar sin^2(θ)=(sin(θ))(sin(θ))	prove\:\sin^{2}(θ)=(\sin(θ))(\sin(θ))
verificar (cos^2(θ))/(sin(θ))+sin(θ)=csc(θ)	prove\:\frac{\cos^{2}(θ)}{\sin(θ)}+\sin(θ)=\csc(θ)
verificar cos(4t)=1-8sin^2(t)cos^2(t)	prove\:\cos(4t)=1-8\sin^{2}(t)\cos^{2}(t)
verificar sin(105)=sin(60+45)	prove\:\sin(105^{\circ\:})=\sin(60^{\circ\:}+45^{\circ\:})
verificar cos(θ)=sin(θ+pi/2)	prove\:\cos(θ)=\sin(θ+\frac{π}{2})
verificar cos^3(x)=sin(x)	prove\:\cos^{3}(x)=\sin(x)
verificar sin(θ)=-5/12	prove\:\sin(θ)=-\frac{5}{12}
verificar tan(pi/3)=sqrt(3)	prove\:\tan(\frac{π}{3})=\sqrt{3}
verificar (1+tan^2(x))/(sec(x))=sec(x)	prove\:\frac{1+\tan^{2}(x)}{\sec(x)}=\sec(x)
verificar sec(0)sin(0)=tan(0)	prove\:\sec(0)\sin(0)=\tan(0)
verificar sec(x)=(tan(x))/(sin(x))	prove\:\sec(x)=\frac{\tan(x)}{\sin(x)}
verificar tan^2(x)=(sec^2(x))/(csc^2(x))	prove\:\tan^{2}(x)=\frac{\sec^{2}(x)}{\csc^{2}(x)}
verificar tan(x)cot(x)sin(x)=csc(x)	prove\:\tan(x)\cot(x)\sin(x)=\csc(x)
verificar 7/(tan(x))+7/(cot(x))=7tan(x)+7cot(x)	prove\:\frac{7}{\tan(x)}+\frac{7}{\cot(x)}=7\tan(x)+7\cot(x)
verificar 1+sin^2(x)=cos^2(x)	prove\:1+\sin^{2}(x)=\cos^{2}(x)
verificar 4tan(x)+2sin(x)cos(x)=0	prove\:4\tan(x)+2\sin(x)\cos(x)=0
verificar 2cos^2(x)-3cos(x)+1=0	prove\:2\cos^{2}(x)-3\cos(x)+1=0
verificar cos(87*pi/2+7/11)=sin(7/11)	prove\:\cos(87\cdot\:\frac{π}{2}+\frac{7}{11})=\sin(\frac{7}{11})
verificar sin^2(θ)+2cos(θ)-1=cos(θ)	prove\:\sin^{2}(θ)+2\cos(θ)-1=\cos(θ)
verificar cos(a-b)=cos(a)cos(b)+sin(a)sin(b)	prove\:\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)
verificar 1+cos^2(x)csc^2(x)= 1/(sin^2(x))	prove\:1+\cos^{2}(x)\csc^{2}(x)=\frac{1}{\sin^{2}(x)}
verificar (csc^2(t))/(1+tan^2(t))=cot^2(t)	prove\:\frac{\csc^{2}(t)}{1+\tan^{2}(t)}=\cot^{2}(t)
verificar sin(x)cos(x)=sin(2x)	prove\:\sin(x)\cos(x)=\sin(2x)
verificar tan(x)+cot(x)=sec(x)cos(x)	prove\:\tan(x)+\cot(x)=\sec(x)\cos(x)

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