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Problemas populares de Trigonometría

verificar (cos(a))/(sec(2a))-(sin(a))/(csc(2a))=cos(3a)	prove\:\frac{\cos(a)}{\sec(2a)}-\frac{\sin(a)}{\csc(2a)}=\cos(3a)
verificar-cos^2(x)tan^2(x)=-sin^2(x)	prove\:-\cos^{2}(x)\tan^{2}(x)=-\sin^{2}(x)
verificar sin(x)-1/(sin(x))=-cos(x)cot(x)	prove\:\sin(x)-\frac{1}{\sin(x)}=-\cos(x)\cot(x)
verificar 2cos^2(x)-cos(x)-1=0	prove\:2\cos^{2}(x)-\cos(x)-1=0
verificar cos(θ)=cot(θ)sin^2(θ)csc(θ)	prove\:\cos(θ)=\cot(θ)\sin^{2}(θ)\csc(θ)
verificar (cos(x)cot(x))/(1-sin(x))=csc(x)+1	prove\:\frac{\cos(x)\cot(x)}{1-\sin(x)}=\csc(x)+1
verificar (1-cos^2(A))(1+cot^2(A))=1	prove\:(1-\cos^{2}(A))(1+\cot^{2}(A))=1
verificar 4cos^2(x)+cos(2x)=5-6sin^2(x)	prove\:4\cos^{2}(x)+\cos(2x)=5-6\sin^{2}(x)
verificar (sin^2(2x))/4 =sin^2(x)cos^2(x)	prove\:\frac{\sin^{2}(2x)}{4}=\sin^{2}(x)\cos^{2}(x)
verificar 20cos^2(x)-cos(x)-1=0	prove\:20\cos^{2}(x)-\cos(x)-1=0
verificar ((sin(x)+cos(x))^2)/(sin(x)cos(x))=2+csc(x)sec(x)	prove\:\frac{(\sin(x)+\cos(x))^{2}}{\sin(x)\cos(x)}=2+\csc(x)\sec(x)
verificar tan(y/2)=csc(y)-cot(y)	prove\:\tan(\frac{y}{2})=\csc(y)-\cot(y)
verificar sin^2(θ)+1=-2-cos^2(x)	prove\:\sin^{2}(θ)+1=-2-\cos^{2}(x)
verificar sec(x)cot(x)-sin(x)=cos(x)cot(x)	prove\:\sec(x)\cdot\:\cot(x)-\sin(x)=\cos(x)\cdot\:\cot(x)
verificar (cos(θ))/(sec(θ)+tan(θ))=1-sin(θ)	prove\:\frac{\cos(θ)}{\sec(θ)+\tan(θ)}=1-\sin(θ)
verificar (sec(θ))/(tan(θ)+cot(θ))=sin(θ)	prove\:\frac{\sec(θ)}{\tan(θ)+\cot(θ)}=\sin(θ)
verificar 1/(cos^2(x))-2=0	prove\:\frac{1}{\cos^{2}(x)}-2=0
verificar sin(θ)=cos^2(θ)+cos^2(θ)*sin(θ)	prove\:\sin(θ)=\cos^{2}(θ)+\cos^{2}(θ)\cdot\:\sin(θ)
verificar sin(a)=tan(a)cos(a)	prove\:\sin(a)=\tan(a)\cos(a)
verificar cos(x)sec(x)-sin^2(x)=cos^2(x)	prove\:\cos(x)\sec(x)-\sin^{2}(x)=\cos^{2}(x)
verificar (sin(2x))/(cos(2x)+sin^2(x))=2tan(x)	prove\:\frac{\sin(2x)}{\cos(2x)+\sin^{2}(x)}=2\tan(x)
verificar tan(θ)sec(θ)(csc(θ)-sin(θ))=1	prove\:\tan(θ)\sec(θ)(\csc(θ)-\sin(θ))=1
verificar 7cos^2(x)+5sin^2(x)=6+cos(2x)	prove\:7\cos^{2}(x)+5\sin^{2}(x)=6+\cos(2x)
verificar (1-sin^2(A))(1+tan^2(A))=1	prove\:(1-\sin^{2}(A))(1+\tan^{2}(A))=1
verificar 2/(1-cos(2x))=csc^2(x)	prove\:\frac{2}{1-\cos(2x)}=\csc^{2}(x)
verificar sin^4(θ)+cos^2(θ)sin^2(θ)=sin^2(θ)	prove\:\sin^{4}(θ)+\cos^{2}(θ)\sin^{2}(θ)=\sin^{2}(θ)
verificar cos(10x)-cos(6x)=-2sin(8x)sin(2x)	prove\:\cos(10x)-\cos(6x)=-2\sin(8x)\sin(2x)
verificar cot(2x)=(tan(x)(cot^2(x)-1))/2	prove\:\cot(2x)=\frac{\tan(x)(\cot^{2}(x)-1)}{2}
verificar (1+cos(2x))/(cos(x))=2cos(x)	prove\:\frac{1+\cos(2x)}{\cos(x)}=2\cos(x)
verificar sec(y)-cos(y)=tan(y)sin(y)	prove\:\sec(y)-\cos(y)=\tan(y)\sin(y)
verificar csc(x)-sin(x)=cot(x)-cos(x)	prove\:\csc(x)-\sin(x)=\cot(x)-\cos(x)
verificar sin^4(β)-cos^4(β)=2sin^2(β)-1	prove\:\sin^{4}(β)-\cos^{4}(β)=2\sin^{2}(β)-1
verificar 3+cos(2y)=2+2cos^2(y)	prove\:3+\cos(2y)=2+2\cos^{2}(y)
verificar (1-sin^4(x))/(cos^4(x))=1+2tan(x)	prove\:\frac{1-\sin^{4}(x)}{\cos^{4}(x)}=1+2\tan(x)
verificar cos(x)arcsin(x)=(cos(x))/(sin(x))	prove\:\cos(x)\arcsin(x)=\frac{\cos(x)}{\sin(x)}
verificar (sin(pi-x))/(sin(pi/2-x))=tan(x)	prove\:\frac{\sin(π-x)}{\sin(\frac{π}{2}-x)}=\tan(x)
verificar sin(5x)-sin(3x)=2cos(4x)sin(x)	prove\:\sin(5x)-\sin(3x)=2\cos(4x)\sin(x)
verificar 4sin(t)cos^2(t)=sin(t)+sin(3t)	prove\:4\sin(t)\cos^{2}(t)=\sin(t)+\sin(3t)
verificar sin(x)sec(x)+cos(x)sec(x)=sec^2(x)	prove\:\sin(x)\sec(x)+\cos(x)\sec(x)=\sec^{2}(x)
verificar sqrt(81-9(3sin(x))^2)=sec^4(x)	prove\:\sqrt{81-9(3\sin(x))^{2}}=\sec^{4}(x)
verificar sin(40)=2sin(20)cos(20)	prove\:\sin(40^{\circ\:})=2\sin(20^{\circ\:})\cos(20^{\circ\:})
verificar sin(θ)-cos^2(θ)sin(θ)=sin^3(θ)	prove\:\sin(θ)-\cos^{2}(θ)\sin(θ)=\sin^{3}(θ)
verificar 9/(sec(x)+1)-9/(sec(x)-1)=0	prove\:\frac{9}{\sec(x)+1}-\frac{9}{\sec(x)-1}=0
verificar sec^2(x)+csc^2(x)=(sec(x)csc(x))^2	prove\:\sec^{2}(x)+\csc^{2}(x)=(\sec(x)\csc(x))^{2}
verificar tan(x)=(sin(x)csc(x))/(cot(x))	prove\:\tan(x)=\frac{\sin(x)\csc(x)}{\cot(x)}
verificar tan(x)sec(x)cos(x)=tan(x)	prove\:\tan(x)\sec(x)\cos(x)=\tan(x)
verificar (1+sin(x))/(sin(x))=1+csc(x)	prove\:\frac{1+\sin(x)}{\sin(x)}=1+\csc(x)
verificar cos(2y)=(1-tan^2(y))/(1+tan^2(y))	prove\:\cos(2y)=\frac{1-\tan^{2}(y)}{1+\tan^{2}(y)}
verificar sin(θ)cot^2(θ)=cos^2(θ)csc(θ)	prove\:\sin(θ)\cot^{2}(θ)=\cos^{2}(θ)\csc(θ)
verificar (sec(x)tan(x))/(sec^2(x))=sin(x)	prove\:\frac{\sec(x)\tan(x)}{\sec^{2}(x)}=\sin(x)
verificar sin(α)= 1/(csc(α))	prove\:\sin(α)=\frac{1}{\csc(α)}
verificar sin(2x)=1-cos(2x)	prove\:\sin(2x)=1-\cos(2x)
verificar 5sec^2(x)+4=9sec^2(x)-4tan^2(x)	prove\:5\sec^{2}(x)+4=9\sec^{2}(x)-4\tan^{2}(x)
verificar csc(-x)-sin(-x)=cos(x)cot(x)	prove\:\csc(-x)-\sin(-x)=\cos(x)\cot(x)
verificar cos(20pi-x)+sin((83pi)/2+x)=0	prove\:\cos(20π-x)+\sin(\frac{83π}{2}+x)=0
verificar 1/(cot(a)+tan(a))=sin(a)cos(a)	prove\:\frac{1}{\cot(a)+\tan(a)}=\sin(a)\cos(a)
verificar sin(x)sin(2x)+cos(x)cos(2x)=cos(x)	prove\:\sin(x)\sin(2x)+\cos(x)\cos(2x)=\cos(x)
verificar 45-25sin(-120pit)=45+25sin(120pit)	prove\:45-25\sin(-120πt)=45+25\sin(120πt)
verificar (cot^2(x)-1)/(cot^2(x)+1)=cos(2x)	prove\:\frac{\cot^{2}(x)-1}{\cot^{2}(x)+1}=\cos(2x)
verificar cos^2(x)-sin^2(y)=1-2sin^2(y)	prove\:\cos^{2}(x)-\sin^{2}(y)=1-2\sin^{2}(y)
verificar sin(x)+(cos^2(x))/(sin(x))=csc(x)	prove\:\sin(x)+\frac{\cos^{2}(x)}{\sin(x)}=\csc(x)
verificar (cos(x)+1)/(sin(x)+tan(x))=cot(x)	prove\:\frac{\cos(x)+1}{\sin(x)+\tan(x)}=\cot(x)
verificar sin(3x)+sin(x)=2sin(2x)cos(x)	prove\:\sin(3x)+\sin(x)=2\sin(2x)\cos(x)
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 tan^2(A)+1=(sec(A))/(cos(A))	prove\:\tan^{2}(A)+1=\frac{\sec(A)}{\cos(A)}
verificar (2cot(x))/(1+cot^2(x))=sin(2x)	prove\:\frac{2\cot(x)}{1+\cot^{2}(x)}=\sin(2x)
verificar tan^2(x)-sin^2(x)=tan(x)sin(x)	prove\:\tan^{2}(x)-\sin^{2}(x)=\tan(x)\sin(x)
verificar sec(-x)=-sec(x)	prove\:\sec(-x)=-\sec(x)
verificar ((sin^2(x)))/(1-cos(x))=1+cos(x)	prove\:\frac{(\sin^{2}(x))}{1-\cos(x)}=1+\cos(x)
verificar cos(x)(tan^{(2)}(x)+1)=sec(x)	prove\:\cos(x)(\tan^{(2)}(x)+1)=\sec(x)
verificar (tan(x)+cot(x))sin(x)cos(x)=1	prove\:(\tan(x)+\cot(x))\sin(x)\cos(x)=1
verificar (cos(x)+sin(x))^2=1+2sin(x)cos(x)	prove\:(\cos(x)+\sin(x))^{2}=1+2\sin(x)\cos(x)
verificar sin(2x)=(2tan(x))/((1+tan^2(x)))	prove\:\sin(2x)=\frac{2\tan(x)}{(1+\tan^{2}(x))}
verificar 1-cos^2(x)+sqrt(3)=2sin(x)+sqrt(3)	prove\:1-\cos^{2}(x)+\sqrt{3}=2\sin(x)+\sqrt{3}
verificar 5csc(2x)=(5csc(x))/(2cos(x))	prove\:5\csc(2x)=\frac{5\csc(x)}{2\cos(x)}
verificar (-1+sec^2(a))/(-tan(a))=-tan(a)	prove\:\frac{-1+\sec^{2}(a)}{-\tan(a)}=-\tan(a)
verificar tan^2(x)(1+cos(2x))=sin^2(x)	prove\:\tan^{2}(x)(1+\cos(2x))=\sin^{2}(x)
verificar (tan(x))/(csc(x))= 1/(cos(x))-1/(sec(x))	prove\:\frac{\tan(x)}{\csc(x)}=\frac{1}{\cos(x)}-\frac{1}{\sec(x)}
verificar (sin^2(2x))/(1-cos(2x))=2cos^2(x)	prove\:\frac{\sin^{2}(2x)}{1-\cos(2x)}=2\cos^{2}(x)
verificar tan(θ)sec^2(θ)tan(θ)=tan^3(θ)	prove\:\tan(θ)\sec^{2}(θ)\tan(θ)=\tan^{3}(θ)
verificar 1-2sin^2(x/4)=cos(x/2)	prove\:1-2\sin^{2}(\frac{x}{4})=\cos(\frac{x}{2})
verificar cos^2(b)+sin^2(b)=1	prove\:\cos^{2}(b)+\sin^{2}(b)=1
verificar tan(a)sin(a)+cos(a)=sec(a)	prove\:\tan(a)\sin(a)+\cos(a)=\sec(a)
verificar sin((3pi)/4)=sin(3/4 pi+2pi)	prove\:\sin(\frac{3π}{4})=\sin(\frac{3}{4}π+2π)
verificar (cos(θ)+cos(3θ))/(2cos(θ))=cos(2θ)	prove\:\frac{\cos(θ)+\cos(3θ)}{2\cos(θ)}=\cos(2θ)
verificar (cos(x)+cot(x))/(1+csc(x))=cos(x)	prove\:\frac{\cos(x)+\cot(x)}{1+\csc(x)}=\cos(x)
verificar (sin(x)+1)^2+cos^2(x)=2sin(x)+2	prove\:(\sin(x)+1)^{2}+\cos^{2}(x)=2\sin(x)+2
verificar 3tan(x)=4sin(x)	prove\:3\tan(x)=4\sin(x)
verificar sin(x)+cos(x)=sqrt(2)sin(x+pi/4)	prove\:\sin(x)+\cos(x)=\sqrt{2}\sin(x+\frac{π}{4})
verificar (sin(t))cot(t)=cos(t)	prove\:(\sin(t))\cot(t)=\cos(t)
verificar (1-tan^2(x))*cos^2(x)=cos(2x)	prove\:(1-\tan^{2}(x))\cdot\:\cos^{2}(x)=\cos(2x)
verificar cot^2(x)-1=tan^2(x)	prove\:\cot^{2}(x)-1=\tan^{2}(x)
verificar sin^2(θ)+1=-1-cos^2(x)	prove\:\sin^{2}(θ)+1=-1-\cos^{2}(x)
verificar cos(θ)=sqrt(1-sin^2(θ))	prove\:\cos(θ)=\sqrt{1-\sin^{2}(θ)}
verificar (sec(θ)-cos(θ))/(tan(θ))=sin(θ)	prove\:\frac{\sec(θ)-\cos(θ)}{\tan(θ)}=\sin(θ)
verificar 2sin((3pi)/2)=-2+cos((3pi)/2)	prove\:2\sin(\frac{3π}{2})=-2+\cos(\frac{3π}{2})
verificar (sec(x)-tan(x))^2=tan(x)cot(x)	prove\:(\sec(x)-\tan(x))^{2}=\tan(x)\cot(x)
verificar sin(x)=(tan(x)cot(x))/(csc(x))	prove\:\sin(x)=\frac{\tan(x)\cot(x)}{\csc(x)}
verificar cos(x)-sec(x)=cos(x)-1/(cos(x))	prove\:\cos(x)-\sec(x)=\cos(x)-\frac{1}{\cos(x)}
verificar (cot^3(t))/(csc(t))=cos(t)cot^2(t)	prove\:\frac{\cot^{3}(t)}{\csc(t)}=\cos(t)\cot^{2}(t)

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