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Problemas populares de Trigonometría

verificar (tan(x)-cot(x))/(tan(x)+cot(x))=1-2cos^2(x)	prove\:\frac{\tan(x)-\cot(x)}{\tan(x)+\cot(x)}=1-2\cos^{2}(x)
verificar tan(θ)cos(θ)=sin(θ)	prove\:\tan(θ)\cos(θ)=\sin(θ)
verificar (sin(x+pi/2))/(sin(pi-x))=cot(x)	prove\:\frac{\sin(x+\frac{π}{2})}{\sin(π-x)}=\cot(x)
verificar tan(θ)+(cos(θ))/(1+sin(θ))=sec(θ)	prove\:\tan(θ)+\frac{\cos(θ)}{1+\sin(θ)}=\sec(θ)
verificar (sec^2(θ))/(sec^2(θ)-1)=csc^2(θ)	prove\:\frac{\sec^{2}(θ)}{\sec^{2}(θ)-1}=\csc^{2}(θ)
verificar sin^2(x)=cos(x)sin(x)tan(x)	prove\:\sin^{2}(x)=\cos(x)\sin(x)\tan(x)
verificar (cot^2(t))/(csc(t))=csc(t)-sin(t)	prove\:\frac{\cot^{2}(t)}{\csc(t)}=\csc(t)-\sin(t)
verificar cos(pi-θ)=-cos(θ)	prove\:\cos(π-θ)=-\cos(θ)
verificar csc(x)cos^2(x)+sin(x)=csc(x)	prove\:\csc(x)\cos^{2}(x)+\sin(x)=\csc(x)
verificar cot(x)+tan(x)=csc(x)sec(x)	prove\:\cot(x)+\tan(x)=\csc(x)\sec(x)
verificar (sec(θ)-1)/(1-cos(θ))=sec(θ)	prove\:\frac{\sec(θ)-1}{1-\cos(θ)}=\sec(θ)
verificar cot(θ)+tan(θ)=sec(θ)csc(θ)	prove\:\cot(θ)+\tan(θ)=\sec(θ)\csc(θ)
verificar cos(pi/2-θ)=sin(θ)	prove\:\cos(\frac{π}{2}-θ)=\sin(θ)
verificar cos(x)cot(x)+sin(x)=csc(x)	prove\:\cos(x)\cot(x)+\sin(x)=\csc(x)
verificar sin(θ)tan(θ)+cos(θ)=sec(θ)	prove\:\sin(θ)\tan(θ)+\cos(θ)=\sec(θ)
verificar (sin(x))/(csc(x)-cot(x))=1+cos(x)	prove\:\frac{\sin(x)}{\csc(x)-\cot(x)}=1+\cos(x)
verificar cos^4(θ)-sin^4(θ)=cos(2θ)	prove\:\cos^{4}(θ)-\sin^{4}(θ)=\cos(2θ)
verificar cot^2(y)-cos^2(y)=cot^2(y)cos^2(y)	prove\:\cot^{2}(y)-\cos^{2}(y)=\cot^{2}(y)\cos^{2}(y)
verificar cot^2(x)=(csc(x)-1)(csc(x)+1)	prove\:\cot^{2}(x)=(\csc(x)-1)(\csc(x)+1)
verificar sin(θ)-sin(θ)cos^2(θ)=sin^3(θ)	prove\:\sin(θ)-\sin(θ)\cos^{2}(θ)=\sin^{3}(θ)
verificar sin(x+pi/2)=cos(x)	prove\:\sin(x+\frac{π}{2})=\cos(x)
verificar csc^4(x)-cot^4(x)=2csc^2(x)-1	prove\:\csc^{4}(x)-\cot^{4}(x)=2\csc^{2}(x)-1
verificar csc^4(x)-2csc^2(x)+1=cot^4(x)	prove\:\csc^{4}(x)-2\csc^{2}(x)+1=\cot^{4}(x)
verificar (cos(x))/(1-sin(x))+(1-sin(x))/(cos(x))=2sec(x)	prove\:\frac{\cos(x)}{1-\sin(x)}+\frac{1-\sin(x)}{\cos(x)}=2\sec(x)
verificar (tan(θ)cot(θ))/(csc(θ))=sin(θ)	prove\:\frac{\tan(θ)\cot(θ)}{\csc(θ)}=\sin(θ)
verificar (1-cos(x))(1+cos(x))= 1/(csc^2(x))	prove\:(1-\cos(x))(1+\cos(x))=\frac{1}{\csc^{2}(x)}
verificar csc(x)cos(x)=cot(x)	prove\:\csc(x)\cos(x)=\cot(x)
verificar sin(pi-x)=sin(x)	prove\:\sin(π-x)=\sin(x)
verificar (sin(2θ))/(1-cos(2θ))=cot(θ)	prove\:\frac{\sin(2θ)}{1-\cos(2θ)}=\cot(θ)
verificar tan^2(x)=(sin^2(x))/(cos^2(x))	prove\:\tan^{2}(x)=\frac{\sin^{2}(x)}{\cos^{2}(x)}
verificar cos(θ)+sin(θ)tan(θ)=sec(θ)	prove\:\cos(θ)+\sin(θ)\tan(θ)=\sec(θ)
verificar sin^4(θ)-cos^4(θ)=2sin^2(θ)-1	prove\:\sin^{4}(θ)-\cos^{4}(θ)=2\sin^{2}(θ)-1
verificar (sec(θ)-tan(θ))(csc(θ)+1)=cot(θ)	prove\:(\sec(θ)-\tan(θ))(\csc(θ)+1)=\cot(θ)
verificar sin(2θ)=(2tan(θ))/(1+tan^2(θ))	prove\:\sin(2θ)=\frac{2\tan(θ)}{1+\tan^{2}(θ)}
verificar cos(θ)csc(θ)=cot(θ)	prove\:\cos(θ)\csc(θ)=\cot(θ)
verificar sin(x-y)+sin(x+y)=2sin(x)cos(y)	prove\:\sin(x-y)+\sin(x+y)=2\sin(x)\cos(y)
verificar cot(-x)sin(x)=-cos(x)	prove\:\cot(-x)\sin(x)=-\cos(x)
verificar (1+tan^2(x))/(1-tan^2(x))=sec(2x)	prove\:\frac{1+\tan^{2}(x)}{1-\tan^{2}(x)}=\sec(2x)
verificar sin(3pi-x)=sin(x)	prove\:\sin(3π-x)=\sin(x)
verificar sin^2(θ)=(1-cos(2θ))/2	prove\:\sin^{2}(θ)=\frac{1-\cos(2θ)}{2}
verificar sin(3x)=4sin(x)cos^2(x)-sin(x)	prove\:\sin(3x)=4\sin(x)\cos^{2}(x)-\sin(x)
verificar (1+cot(x))^2=csc^2(x)+2cot(x)	prove\:(1+\cot(x))^{2}=\csc^{2}(x)+2\cot(x)
verificar sec(x)-tan(x)sin(x)=cos(x)	prove\:\sec(x)-\tan(x)\sin(x)=\cos(x)
verificar sin(θ)cot(θ)=cos(θ)	prove\:\sin(θ)\cot(θ)=\cos(θ)
verificar tan(θ)csc(θ)cos(θ)=1	prove\:\tan(θ)\csc(θ)\cos(θ)=1
verificar 1+tan^2(θ)=sec^2(θ)	prove\:1+\tan^{2}(θ)=\sec^{2}(θ)
verificar (sin(pi-x))/(sin(x+pi/2))=tan(x)	prove\:\frac{\sin(π-x)}{\sin(x+\frac{π}{2})}=\tan(x)
verificar (cos^2(x))/(1-sin(x))=(csc(x)+1)/(csc(x))	prove\:\frac{\cos^{2}(x)}{1-\sin(x)}=\frac{\csc(x)+1}{\csc(x)}
verificar cos(3x)=cos^3(x)-3sin^2(x)cos(x)	prove\:\cos(3x)=\cos^{3}(x)-3\sin^{2}(x)\cos(x)
verificar tan(x)(1+cos(2x))=sin(2x)	prove\:\tan(x)(1+\cos(2x))=\sin(2x)
verificar (sin(x)+tan(x))/(1+sec(x))=sin(x)	prove\:\frac{\sin(x)+\tan(x)}{1+\sec(x)}=\sin(x)
verificar (sec(x)-tan(x))(csc(x)+1)=cot(x)	prove\:(\sec(x)-\tan(x))(\csc(x)+1)=\cot(x)
verificar (1-sin^2(x))(1+tan^2(x))=1	prove\:(1-\sin^{2}(x))(1+\tan^{2}(x))=1
verificar 1/(sec(x)+1)+1/(cos(x)+1)=1	prove\:\frac{1}{\sec(x)+1}+\frac{1}{\cos(x)+1}=1
verificar (1-sin^4(x))/(cos^2(x))=2-cos^2(x)	prove\:\frac{1-\sin^{4}(x)}{\cos^{2}(x)}=2-\cos^{2}(x)
verificar (1+cot^2(x))tan(x)=csc(x)sec(x)	prove\:(1+\cot^{2}(x))\tan(x)=\csc(x)\sec(x)
verificar tan(x)cos(x)=sin(x)	prove\:\tan(x)\cos(x)=\sin(x)
verificar (cos^2(x))/(1+sin(x))=1-sin(x)	prove\:\frac{\cos^{2}(x)}{1+\sin(x)}=1-\sin(x)
verificar sin(a+b)+sin(a-b)=2sin(a)cos(b)	prove\:\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)
verificar (cos(x))(1+tan(x))^2=sec(x)+2sin(x)	prove\:(\cos(x))(1+\tan(x))^{2}=\sec(x)+2\sin(x)
verificar (1+tan^2(x))/(2tan(x))=csc(2x)	prove\:\frac{1+\tan^{2}(x)}{2\tan(x)}=\csc(2x)
verificar cos(3θ)=cos^3(θ)-3cos(θ)sin^2(θ)	prove\:\cos(3θ)=\cos^{3}(θ)-3\cos(θ)\sin^{2}(θ)
verificar (tan^2(x))/(sec(x))=sin(x)tan(x)	prove\:\frac{\tan^{2}(x)}{\sec(x)}=\sin(x)\tan(x)
verificar cot(x)(1-cos(2x))=sin(2x)	prove\:\cot(x)(1-\cos(2x))=\sin(2x)
verificar tan(θ)cot(θ)=1	prove\:\tan(θ)\cot(θ)=1
verificar cos(pi/2-x)=sin(x)	prove\:\cos(\frac{π}{2}-x)=\sin(x)
verificar sin(pi/2-θ)=cos(θ)	prove\:\sin(\frac{π}{2}-θ)=\cos(θ)
verificar cot^2(x)+1=csc^2(x)	prove\:\cot^{2}(x)+1=\csc^{2}(x)
verificar sec(u)-tan(u)=(cos(u))/(1+sin(u))	prove\:\sec(u)-\tan(u)=\frac{\cos(u)}{1+\sin(u)}
verificar (sec^2(x))/(tan(x))=sec(x)csc(x)	prove\:\frac{\sec^{2}(x)}{\tan(x)}=\sec(x)\csc(x)
verificar cot(x)+(sin(x))/(1+cos(x))=csc(x)	prove\:\cot(x)+\frac{\sin(x)}{1+\cos(x)}=\csc(x)
verificar (sec^2(θ)-1)/(sec^2(θ))=sin^2(θ)	prove\:\frac{\sec^{2}(θ)-1}{\sec^{2}(θ)}=\sin^{2}(θ)
verificar cos(x)-cos(3x)=4sin^2(x)cos(x)	prove\:\cos(x)-\cos(3x)=4\sin^{2}(x)\cos(x)
verificar cot(x)=(1+cos(2x))/(sin(2x))	prove\:\cot(x)=\frac{1+\cos(2x)}{\sin(2x)}
verificar (sin(x))/(tan(x))=cos(x)	prove\:\frac{\sin(x)}{\tan(x)}=\cos(x)
verificar (csc^2(x))/(2cot(x))=csc(2x)	prove\:\frac{\csc^{2}(x)}{2\cot(x)}=\csc(2x)
verificar cot(θ)sin(θ)=cos(θ)	prove\:\cot(θ)\sin(θ)=\cos(θ)
verificar cot(x)(sec^2(x)-1)=tan(x)	prove\:\cot(x)(\sec^{2}(x)-1)=\tan(x)
verificar (1-cos(x))(1+cos(x))=sin^2(x)	prove\:(1-\cos(x))(1+\cos(x))=\sin^{2}(x)
verificar (1+sin(θ))(1-sin(θ))=cos^2(θ)	prove\:(1+\sin(θ))(1-\sin(θ))=\cos^{2}(θ)
verificar sin(θ)(tan(θ)+cot(θ))=sec(θ)	prove\:\sin(θ)(\tan(θ)+\cot(θ))=\sec(θ)
verificar cot(2θ)=(cot^2(θ)-1)/(2cot(θ))	prove\:\cot(2θ)=\frac{\cot^{2}(θ)-1}{2\cot(θ)}
verificar (cos(x))/(1-sin(x))-tan(x)=sec(x)	prove\:\frac{\cos(x)}{1-\sin(x)}-\tan(x)=\sec(x)
verificar sin^2(θ)=1-cos^2(θ)	prove\:\sin^{2}(θ)=1-\cos^{2}(θ)
verificar (sec^2(x)-1)cos^2(x)=sin^2(x)	prove\:(\sec^{2}(x)-1)\cos^{2}(x)=\sin^{2}(x)
verificar tan(x)=(1-cos(2x))/(sin(2x))	prove\:\tan(x)=\frac{1-\cos(2x)}{\sin(2x)}
verificar (sec^2(x)-1)cos(x)=sin^2(x)sec(x)	prove\:(\sec^{2}(x)-1)\cos(x)=\sin^{2}(x)\sec(x)
verificar sin^3(x)+sin(x)cos^2(x)=sin(x)	prove\:\sin^{3}(x)+\sin(x)\cos^{2}(x)=\sin(x)
verificar 2/(cot(x)+tan(x))=sin(2x)	prove\:\frac{2}{\cot(x)+\tan(x)}=\sin(2x)
verificar tan(t)+2cos(t)csc(t)=sec(t)csc(t)+cot(t)	prove\:\tan(t)+2\cos(t)\csc(t)=\sec(t)\csc(t)+\cot(t)
verificar 1/(tan(x)(1+cos(2x)))=csc(2x)	prove\:\frac{1}{\tan(x)(1+\cos(2x))}=\csc(2x)
verificar sin^2(x)tan^2(x)=tan^2(x)-sin^2(x)	prove\:\sin^{2}(x)\tan^{2}(x)=\tan^{2}(x)-\sin^{2}(x)
verificar (tan^2(x))/(sec(x)+1)=sec(x)-1	prove\:\frac{\tan^{2}(x)}{\sec(x)+1}=\sec(x)-1
verificar (1-cos(θ))(1+cos(θ))=sin^2(θ)	prove\:(1-\cos(θ))(1+\cos(θ))=\sin^{2}(θ)
verificar (1-3cos(x)-4cos^2(x))/(sin^2(x))=(1-4cos(x))/(1-cos(x))	prove\:\frac{1-3\cos(x)-4\cos^{2}(x)}{\sin^{2}(x)}=\frac{1-4\cos(x)}{1-\cos(x)}
verificar (1+cos(2x))(1-cos(2x))=sin^2(2x)	prove\:(1+\cos(2x))(1-\cos(2x))=\sin^{2}(2x)
verificar (sin(x)csc(x))/(cot(x))=tan(x)	prove\:\frac{\sin(x)\csc(x)}{\cot(x)}=\tan(x)
verificar cos^2(θ)(tan^2(θ)+1)=1	prove\:\cos^{2}(θ)(\tan^{2}(θ)+1)=1
verificar sec^2(θ/2)= 2/(1+cos(θ))	prove\:\sec^{2}(\frac{θ}{2})=\frac{2}{1+\cos(θ)}
verificar 1/(sin(x)+1)+1/(csc(x)+1)=1	prove\:\frac{1}{\sin(x)+1}+\frac{1}{\csc(x)+1}=1

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