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Problemas populares Trigonometría

verificar cos^2(θ/2)=(sec(θ)+1)/(2sec(θ))	prove\:\cos^{2}(\frac{θ}{2})=\frac{\sec(θ)+1}{2\sec(θ)}
verificar cos^2(x)=(cos(x))^2	prove\:\cos^{2}(x)=(\cos(x))^{2}
verificar 2cos^2(θ)tan(θ)=sin(2θ)	prove\:2\cos^{2}(θ)\tan(θ)=\sin(2θ)
verificar sin^5(x)=(1-cos^2(x))^2sin(x)	prove\:\sin^{5}(x)=(1-\cos^{2}(x))^{2}\sin(x)
verificar cos((3pi)/2-x)=-sin(x)	prove\:\cos(\frac{3π}{2}-x)=-\sin(x)
verificar cot(t)+(sin(t))/(1+cos(t))=csc(t)	prove\:\cot(t)+\frac{\sin(t)}{1+\cos(t)}=\csc(t)
verificar csc^2(x)*tan^2(x)-1=tan^2(x)	prove\:\csc^{2}(x)\cdot\:\tan^{2}(x)-1=\tan^{2}(x)
verificar sec^2(x)-cot^2(pi/2-x)=1	prove\:\sec^{2}(x)-\cot^{2}(\frac{π}{2}-x)=1
verificar sin(2x)=-2sin(-x)cos(-x)	prove\:\sin(2x)=-2\sin(-x)\cos(-x)
verificar sin(θ)csc(θ)-sin^2(θ)=cos^2(θ)	prove\:\sin(θ)\csc(θ)-\sin^{2}(θ)=\cos^{2}(θ)
verificar cos^2(x)csc(x)sec(x)=cot(x)	prove\:\cos^{2}(x)\csc(x)\sec(x)=\cot(x)
verificar (cos^2(-x)csc(x))/(cot(x))=cos(x)	prove\:\frac{\cos^{2}(-x)\csc(x)}{\cot(x)}=\cos(x)
verificar cot(2x)=(csc^2(x)-2)/(2cot(x))	prove\:\cot(2x)=\frac{\csc^{2}(x)-2}{2\cot(x)}
verificar 1/(cos(θ))=(tan(θ))/(sin(θ))	prove\:\frac{1}{\cos(θ)}=\frac{\tan(θ)}{\sin(θ)}
verificar sin(x)*tan(x)=sec(x)-cos(x)	prove\:\sin(x)\cdot\:\tan(x)=\sec(x)-\cos(x)
verificar (tan(y)+cot(y))sin(y)cos(y)=1	prove\:(\tan(y)+\cot(y))\sin(y)\cos(y)=1
verificar (csc(θ)-cot(θ))(csc(θ)+cot(θ))=1	prove\:(\csc(θ)-\cot(θ))(\csc(θ)+\cot(θ))=1
verificar 1+sin(x)cot(x)=1+cos(x)	prove\:1+\sin(x)\cot(x)=1+\cos(x)
verificar (1+sin(z))(1-sin(z))= 1/(sec^2(z))	prove\:(1+\sin(z))(1-\sin(z))=\frac{1}{\sec^{2}(z)}
verificar ((1+tan(θ)))/(1+cot(θ))=tan(θ)	prove\:\frac{(1+\tan(θ))}{1+\cot(θ)}=\tan(θ)
verificar-sin^2(x)=cos^2(x)-1	prove\:-\sin^{2}(x)=\cos^{2}(x)-1
verificar (sin(A))/(1-cos(A))-cot(A)=csc(A)	prove\:\frac{\sin(A)}{1-\cos(A)}-\cot(A)=\csc(A)
verificar (tan(x)+cot(x))^2=csc^2(x)sec^2(x)	prove\:(\tan(x)+\cot(x))^{2}=\csc^{2}(x)\sec^{2}(x)
verificar tan(θ/2)=(sin(θ))/(1+cos(θ))	prove\:\tan(\frac{θ}{2})=\frac{\sin(θ)}{1+\cos(θ)}
verificar sin((3pi)/2-x)=-cos(x)	prove\:\sin(\frac{3π}{2}-x)=-\cos(x)
verificar sin(x)sec(x)= 1/(cot(x))	prove\:\sin(x)\sec(x)=\frac{1}{\cot(x)}
verificar (1-cos(2x))/2 =sin^2(x)	prove\:\frac{1-\cos(2x)}{2}=\sin^{2}(x)
verificar (sec(x))/(1-cos(x))=(sec(x)+1)/(sin^2(x))	prove\:\frac{\sec(x)}{1-\cos(x)}=\frac{\sec(x)+1}{\sin^{2}(x)}
verificar tan(pi/4-θ)=(cos(θ)-sin(θ))/(cos(θ)+sin(θ))	prove\:\tan(\frac{π}{4}-θ)=\frac{\cos(θ)-\sin(θ)}{\cos(θ)+\sin(θ)}
verificar cot(2θ)= 1/2 sec(θ)csc(θ)-tan(θ)	prove\:\cot(2θ)=\frac{1}{2}\sec(θ)\csc(θ)-\tan(θ)
verificar 8cos^2(x)-8sin^2(x)=8-16sin^2(x)	prove\:8\cos^{2}(x)-8\sin^{2}(x)=8-16\sin^{2}(x)
verificar sec(x)-sin(x)*tan(x)=cos(x)	prove\:\sec(x)-\sin(x)\cdot\:\tan(x)=\cos(x)
verificar (sec(x)csc(x))/(cot(x))=sec^2(x)	prove\:\frac{\sec(x)\csc(x)}{\cot(x)}=\sec^{2}(x)
verificar (sin(θ)-cos(θ))^2=1-2sin(θ)cos(θ)	prove\:(\sin(θ)-\cos(θ))^{2}=1-2\sin(θ)\cos(θ)
verificar cot(θ)sin(θ)sec(θ)=1	prove\:\cot(θ)\sin(θ)\sec(θ)=1
verificar cos^4(x)=1-2sin^2(x)+sin^4(x)	prove\:\cos^{4}(x)=1-2\sin^{2}(x)+\sin^{4}(x)
verificar (sec(x)+tan(x))/(csc(x)+1)=tan(x)	prove\:\frac{\sec(x)+\tan(x)}{\csc(x)+1}=\tan(x)
verificar sec(x)tan(x)cos(x)cot(x)=1	prove\:\sec(x)\tan(x)\cos(x)\cot(x)=1
verificar 1-sec(x)cos^3(x)=sin^2(x)	prove\:1-\sec(x)\cos^{3}(x)=\sin^{2}(x)
verificar tan(3pi+θ)=tan(θ)	prove\:\tan(3π+θ)=\tan(θ)
verificar 4sin(-x)cos(-x)=-2sin(2x)	prove\:4\sin(-x)\cos(-x)=-2\sin(2x)
verificar sin(x)cos(x)= 1/2 sin(2x)	prove\:\sin(x)\cos(x)=\frac{1}{2}\sin(2x)
verificar 8sin(x)cos(x)=4sin(2x)	prove\:8\sin(x)\cos(x)=4\sin(2x)
verificar sec(a)-cos(a)=sin(a)tan(a)	prove\:\sec(a)-\cos(a)=\sin(a)\tan(a)
verificar (sec(x)+tan(x))(1-sin(x))=cos(x)	prove\:(\sec(x)+\tan(x))(1-\sin(x))=\cos(x)
verificar tan(A)+cot(A)=sec(A)csc(A)	prove\:\tan(A)+\cot(A)=\sec(A)\csc(A)
verificar (cos(x))/(sec(x)-1)-(cos(x))/(sec(x)+1)=(2cos(x))/(tan^2(x))	prove\:\frac{\cos(x)}{\sec(x)-1}-\frac{\cos(x)}{\sec(x)+1}=\frac{2\cos(x)}{\tan^{2}(x)}
verificar (cot(a))/(cos(a))=csc(a)	prove\:\frac{\cot(a)}{\cos(a)}=\csc(a)
verificar cos(2θ)=(2-sec^2(θ))/(sec^2(θ))	prove\:\cos(2θ)=\frac{2-\sec^{2}(θ)}{\sec^{2}(θ)}
verificar (tan(x)+sec(x))(1-sin(x))=cos(x)	prove\:(\tan(x)+\sec(x))(1-\sin(x))=\cos(x)
verificar (csc^4(x)-1)/(cot^2(x))=csc^2(x)+1	prove\:\frac{\csc^{4}(x)-1}{\cot^{2}(x)}=\csc^{2}(x)+1
verificar sin(θ)+cos(θ)=sqrt(2)sin(θ+45)	prove\:\sin(θ)+\cos(θ)=\sqrt{2}\sin(θ+45^{\circ\:})
verificar (1-tan(θ))/(1+tan(θ))=(cot(θ)-1)/(cot(θ)+1)	prove\:\frac{1-\tan(θ)}{1+\tan(θ)}=\frac{\cot(θ)-1}{\cot(θ)+1}
verificar cot(θ)sin(θ)cos(θ)=1-sin^2(θ)	prove\:\cot(θ)\sin(θ)\cos(θ)=1-\sin^{2}(θ)
verificar csc(θ)= 1/(sin(θ))	prove\:\csc(θ)=\frac{1}{\sin(θ)}
verificar 1/(sin(θ))-sin(θ)=cot(θ)cos(θ)	prove\:\frac{1}{\sin(θ)}-\sin(θ)=\cot(θ)\cos(θ)
verificar (sec(-x))/(tan(x)+cot(x))=-sin(-x)	prove\:\frac{\sec(-x)}{\tan(x)+\cot(x)}=-\sin(-x)
verificar (sin(t))/(1-cos(t))=csc(t)+cot(t)	prove\:\frac{\sin(t)}{1-\cos(t)}=\csc(t)+\cot(t)
verificar sin(-x)+cot(-x)cos(-x)=-csc(x)	prove\:\sin(-x)+\cot(-x)\cos(-x)=-\csc(x)
verificar coth^2(x)-csch^2(x)=1	prove\:\coth^{2}(x)-\csch^{2}(x)=1
verificar csc(θ)(1-cos^2(θ))=sin(θ)	prove\:\csc(θ)(1-\cos^{2}(θ))=\sin(θ)
verificar ((csc^2(x)))/(cot(x))=csc(x)sec(x)	prove\:\frac{(\csc^{2}(x))}{\cot(x)}=\csc(x)\sec(x)
verificar csc^2(x)(tan^2(x))-1=tan^2(x)	prove\:\csc^{2}(x)(\tan^{2}(x))-1=\tan^{2}(x)
verificar sin(x)cos(x)+sin(3x)sec(x)=tan(x)	prove\:\sin(x)\cos(x)+\sin(3x)\sec(x)=\tan(x)
verificar (1+sec(x))(1-cos(x))=sin(x)tan(x)	prove\:(1+\sec(x))(1-\cos(x))=\sin(x)\tan(x)
verificar sec(x)*sin(x)=tan(x)	prove\:\sec(x)\cdot\:\sin(x)=\tan(x)
verificar tan(x)csc(x)sec(x)=tan^2(x)+1	prove\:\tan(x)\csc(x)\sec(x)=\tan^{2}(x)+1
verificar 1/(cos(-x))-tan(-x)sin(-x)=cos(x)	prove\:\frac{1}{\cos(-x)}-\tan(-x)\sin(-x)=\cos(x)
verificar cos(15)=cos(45-30)	prove\:\cos(15^{\circ\:})=\cos(45^{\circ\:}-30^{\circ\:})
verificar (sin(2x))/(1-cos(2x))=2csc(2x)-tan(x)	prove\:\frac{\sin(2x)}{1-\cos(2x)}=2\csc(2x)-\tan(x)
verificar tan(x)=tan(x)*csc^2(x)+cot(-x)	prove\:\tan(x)=\tan(x)\cdot\:\csc^{2}(x)+\cot(-x)
verificar (1-cos(2θ)+sin(2θ))/(1+cos(2θ)+sin(2θ))=tan(θ)	prove\:\frac{1-\cos(2θ)+\sin(2θ)}{1+\cos(2θ)+\sin(2θ)}=\tan(θ)
verificar cot(x)sec^2(x)-cot(x)=tan(x)	prove\:\cot(x)\sec^{2}(x)-\cot(x)=\tan(x)
verificar cos(-pi/4-5t)=cos(5t+pi/4)	prove\:\cos(-\frac{π}{4}-5t)=\cos(5t+\frac{π}{4})
verificar tan(pi/4-θ)=(1-tan(θ))/(1+tan(θ))	prove\:\tan(\frac{π}{4}-θ)=\frac{1-\tan(θ)}{1+\tan(θ)}
verificar cos^2(B)= 1/2 (1+cos(2B))	prove\:\cos^{2}(B)=\frac{1}{2}(1+\cos(2B))
verificar sin(θ+pi)=-sin(θ)	prove\:\sin(θ+π)=-\sin(θ)
verificar sin(x+(3pi)/2)=-cos(x)	prove\:\sin(x+\frac{3π}{2})=-\cos(x)
verificar sec(x)-sec(x)*sin^2(x)=cos(x)	prove\:\sec(x)-\sec(x)\cdot\:\sin^{2}(x)=\cos(x)
verificar (2sin(x)cos(x))/(cos(2x))=tan(2x)	prove\:\frac{2\sin(x)\cos(x)}{\cos(2x)}=\tan(2x)
verificar tan(-θ)=-tan(θ)	prove\:\tan(-θ)=-\tan(θ)
verificar tan(θ+pi)=tan(θ)	prove\:\tan(θ+π)=\tan(θ)
verificar cos(pi/6)=(sqrt(3))/2	prove\:\cos(\frac{π}{6})=\frac{\sqrt{3}}{2}
verificar sin(10θ)=2sin(5θ)cos(5θ)	prove\:\sin(10θ)=2\sin(5θ)\cos(5θ)
verificar sin(x)=cos(pi/2-x)	prove\:\sin(x)=\cos(\frac{π}{2}-x)
verificar (sin(x))/(cot(x))=sec(x)-cos(x)	prove\:\frac{\sin(x)}{\cot(x)}=\sec(x)-\cos(x)
verificar sec(2x)= 1/(1-2sin^2(x))	prove\:\sec(2x)=\frac{1}{1-2\sin^{2}(x)}
verificar cos(3θ)+cos(θ)=4cos^3(θ)-2cos(θ)	prove\:\cos(3θ)+\cos(θ)=4\cos^{3}(θ)-2\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+tan(θ))^2=sec^2(θ)+2tan(θ)	prove\:(1+\tan(θ))^{2}=\sec^{2}(θ)+2\tan(θ)
verificar (1-tan(θ))^2=sec^2(θ)-2tan(θ)	prove\:(1-\tan(θ))^{2}=\sec^{2}(θ)-2\tan(θ)
verificar 4sin(x/4)cos(x/4)cos(x/2)=sin(x)	prove\:4\sin(\frac{x}{4})\cos(\frac{x}{4})\cos(\frac{x}{2})=\sin(x)
verificar (sin(θ)+sin(3θ))/(2sin(2θ))=cos(θ)	prove\:\frac{\sin(θ)+\sin(3θ)}{2\sin(2θ)}=\cos(θ)
verificar cos(2A)=1-2sin^2(A)	prove\:\cos(2A)=1-2\sin^{2}(A)
verificar cot(-x)=-cot(x)	prove\:\cot(-x)=-\cot(x)
verificar (csc(t)+1)/(cot(t))=(cot(t))/(csc(t)-1)	prove\:\frac{\csc(t)+1}{\cot(t)}=\frac{\cot(t)}{\csc(t)-1}
verificar (cos(x))/(sin^2(x))=csc(x)cot(x)	prove\:\frac{\cos(x)}{\sin^{2}(x)}=\csc(x)\cot(x)
verificar tan(2x)-tan(x)=tan(x)sec(2x)	prove\:\tan(2x)-\tan(x)=\tan(x)\sec(2x)
verificar cos(2a)=2cos^2(a)-1	prove\:\cos(2a)=2\cos^{2}(a)-1
verificar 1+sec(x)=(cos(x)+1)/(cos(x))	prove\:1+\sec(x)=\frac{\cos(x)+1}{\cos(x)}

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