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Problemas populares Trigonometría

verificar 1/(1+cos(x))+1/(1-cos(x))=2csc^2(x)	prove\:\frac{1}{1+\cos(x)}+\frac{1}{1-\cos(x)}=2\csc^{2}(x)
verificar (csc(-x))/(sec(-x))=-cot(x)	prove\:\frac{\csc(-x)}{\sec(-x)}=-\cot(x)
verificar cos(x-y)+cos(x+y)=2cos(x)cos(y)	prove\:\cos(x-y)+\cos(x+y)=2\cos(x)\cos(y)
verificar sin(pi/6+x)+sin(pi/6-x)=cos(x)	prove\:\sin(\frac{π}{6}+x)+\sin(\frac{π}{6}-x)=\cos(x)
verificar (cot(x)-csc(x))(cos(x)+1)=-sin(x)	prove\:(\cot(x)-\csc(x))(\cos(x)+1)=-\sin(x)
verificar csc^4(θ)-cot^4(θ)=2csc^2(θ)-1	prove\:\csc^{4}(θ)-\cot^{4}(θ)=2\csc^{2}(θ)-1
verificar (cos(θ)cot(θ))/(1-sin(θ))-1=csc(θ)	prove\:\frac{\cos(θ)\cot(θ)}{1-\sin(θ)}-1=\csc(θ)
verificar csc(θ)-sin(θ)=cos(θ)cot(θ)	prove\:\csc(θ)-\sin(θ)=\cos(θ)\cot(θ)
verificar sec(x)(1-sin^2(x))=cos(x)	prove\:\sec(x)(1-\sin^{2}(x))=\cos(x)
verificar (1-cos^2(θ))(1+cot^2(θ))=1	prove\:(1-\cos^{2}(θ))(1+\cot^{2}(θ))=1
verificar cot(x)sin(x)=cos(x)	prove\:\cot(x)\sin(x)=\cos(x)
verificar sin(2x)+cos(2x)-1=2sin(x)(cos(x)-sin(x))	prove\:\sin(2x)+\cos(2x)-1=2\sin(x)(\cos(x)-\sin(x))
verificar (csc^2(x)-1)sin(x)=cot(x)cos(x)	prove\:(\csc^{2}(x)-1)\sin(x)=\cot(x)\cos(x)
verificar cot(x)(1-cos^2(x))= 1/2 sin(2x)	prove\:\cot(x)(1-\cos^{2}(x))=\frac{1}{2}\sin(2x)
verificar (sec^2(t))/(tan(t))=sec(t)csc(t)	prove\:\frac{\sec^{2}(t)}{\tan(t)}=\sec(t)\csc(t)
verificar cos(x)(tan^2(x)+1)=sec(x)	prove\:\cos(x)(\tan^{2}(x)+1)=\sec(x)
verificar csc^2(θ)-cot^2(θ)=1	prove\:\csc^{2}(θ)-\cot^{2}(θ)=1
verificar (sec^2(x)-1)csc^2(x)=sec^2(x)	prove\:(\sec^{2}(x)-1)\csc^{2}(x)=\sec^{2}(x)
verificar (1+sin(a))(1-sin(a))=cos^2(a)	prove\:(1+\sin(a))(1-\sin(a))=\cos^{2}(a)
verificar sin^3(θ)= 3/4 sin(θ)-1/4 sin(3θ)	prove\:\sin^{3}(θ)=\frac{3}{4}\sin(θ)-\frac{1}{4}\sin(3θ)
verificar tan^2(θ)+1=sec^2(θ)	prove\:\tan^{2}(θ)+1=\sec^{2}(θ)
verificar (cos(x)sec(x))/(tan(x))=cot(x)	prove\:\frac{\cos(x)\sec(x)}{\tan(x)}=\cot(x)
verificar (csc^2(t))/(cot(t))=csc(t)sec(t)	prove\:\frac{\csc^{2}(t)}{\cot(t)}=\csc(t)\sec(t)
verificar (2cos(2x))/(sin(2x))=cot(x)-tan(x)	prove\:\frac{2\cos(2x)}{\sin(2x)}=\cot(x)-\tan(x)
verificar cot^2(t)-cos^2(t)=cot^2(t)cos^2(t)	prove\:\cot^{2}(t)-\cos^{2}(t)=\cot^{2}(t)\cos^{2}(t)
verificar cot(θ)=(cos(θ))/(sin(θ))	prove\:\cot(θ)=\frac{\cos(θ)}{\sin(θ)}
verificar (1-cot(x))^2=csc^2(x)-2cot(x)	prove\:(1-\cot(x))^{2}=\csc^{2}(x)-2\cot(x)
verificar 1/(cot(x)(1-cos(2x)))=csc(2x)	prove\:\frac{1}{\cot(x)(1-\cos(2x))}=\csc(2x)
verificar (tan(θ)+cot(θ))cos(θ)=csc(θ)	prove\:(\tan(θ)+\cot(θ))\cos(θ)=\csc(θ)
verificar cos^4(t)-sin^4(t)=1-2sin^2(t)	prove\:\cos^{4}(t)-\sin^{4}(t)=1-2\sin^{2}(t)
verificar 1+tan^2(-θ)=sec^2(θ)	prove\:1+\tan^{2}(-θ)=\sec^{2}(θ)
verificar (tan(x)+tan(y))/(cot(x)+cot(y))=tan(x)tan(y)	prove\:\frac{\tan(x)+\tan(y)}{\cot(x)+\cot(y)}=\tan(x)\tan(y)
verificar (cos(pi/2+x))/(cos(pi+x))=tan(x)	prove\:\frac{\cos(\frac{π}{2}+x)}{\cos(π+x)}=\tan(x)
verificar 1-cos(2x)=tan(x)sin(2x)	prove\:1-\cos(2x)=\tan(x)\sin(2x)
verificar 1=sec^2(2x)-tan^2(2x)	prove\:1=\sec^{2}(2x)-\tan^{2}(2x)
verificar 2cot(2x)=cot(x)-tan(x)	prove\:2\cot(2x)=\cot(x)-\tan(x)
verificar cos(pi/2+x)=-sin(x)	prove\:\cos(\frac{π}{2}+x)=-\sin(x)
verificar cos(x)=cos(-x)	prove\:\cos(x)=\cos(-x)
verificar 1/(cot(x)+1)+1/(tan(x)+1)=1	prove\:\frac{1}{\cot(x)+1}+\frac{1}{\tan(x)+1}=1
verificar csc(x)tan(x)=sec(x)	prove\:\csc(x)\tan(x)=\sec(x)
verificar 1+cot^2(x)= 1/(sin^2(x))	prove\:1+\cot^{2}(x)=\frac{1}{\sin^{2}(x)}
verificar tan(θ)cot(θ)-sin^2(θ)=cos^2(θ)	prove\:\tan(θ)\cot(θ)-\sin^{2}(θ)=\cos^{2}(θ)
verificar sin(2x)=(2cot(x))/(1+cot^2(x))	prove\:\sin(2x)=\frac{2\cot(x)}{1+\cot^{2}(x)}
verificar sec(θ)= 1/(cos(θ))	prove\:\sec(θ)=\frac{1}{\cos(θ)}
verificar csc(2θ)=(csc(θ))/(2cos(θ))	prove\:\csc(2θ)=\frac{\csc(θ)}{2\cos(θ)}
verificar sin(-x)+csc(x)=cot(x)cos(x)	prove\:\sin(-x)+\csc(x)=\cot(x)\cos(x)
verificar sin(x+y)=sin(x)cos(y)+cos(x)sin(y)	prove\:\sin(x+y)=\sin(x)\cos(y)+\cos(x)\sin(y)
verificar sin(u)csc(u)-cos^2(u)=sin^2(u)	prove\:\sin(u)\csc(u)-\cos^{2}(u)=\sin^{2}(u)
verificar 1-tan^2(x)=(cos(2x))/(cos^2(x))	prove\:1-\tan^{2}(x)=\frac{\cos(2x)}{\cos^{2}(x)}
verificar sin^2(-θ)+cos^2(-θ)=1	prove\:\sin^{2}(-θ)+\cos^{2}(-θ)=1
verificar sin(2x)=sin(x+x)	prove\:\sin(2x)=\sin(x+x)
verificar 8cos^4(x)-8cos^2(x)+1=cos(4x)	prove\:8\cos^{4}(x)-8\cos^{2}(x)+1=\cos(4x)
verificar (cos(2x)-cos(4x))/(sin(2x)sin(4x))=tan(x)	prove\:\frac{\cos(2x)-\cos(4x)}{\sin(2x)\sin(4x)}=\tan(x)
verificar (tan(x)+cot(x))/(csc(x))=sec(x)	prove\:\frac{\tan(x)+\cot(x)}{\csc(x)}=\sec(x)
verificar tan(-x)=-tan(x)	prove\:\tan(-x)=-\tan(x)
verificar cot(θ)=(sin(2θ))/(1-cos(2θ))	prove\:\cot(θ)=\frac{\sin(2θ)}{1-\cos(2θ)}
verificar (sec^2(x)-1)cos(x)=tan(x)sin(x)	prove\:(\sec^{2}(x)-1)\cos(x)=\tan(x)\sin(x)
verificar cot(x)= 1/(tan(x))	prove\:\cot(x)=\frac{1}{\tan(x)}
verificar sec(-x)sin(x)=tan(x)	prove\:\sec(-x)\sin(x)=\tan(x)
verificar (cos^2(v))/(sin(v))=csc(v)-sin(v)	prove\:\frac{\cos^{2}(v)}{\sin(v)}=\csc(v)-\sin(v)
verificar sin(2x)=2cot(x)sin^2(x)	prove\:\sin(2x)=2\cot(x)\sin^{2}(x)
verificar (sec(t)-cos(t))/(sec(t))=sin^2(t)	prove\:\frac{\sec(t)-\cos(t)}{\sec(t)}=\sin^{2}(t)
verificar 1/(tan(x))+tan(x)=sec(x)csc(x)	prove\:\frac{1}{\tan(x)}+\tan(x)=\sec(x)\csc(x)
verificar tan(θ)+cot(θ)=2csc(2θ)	prove\:\tan(θ)+\cot(θ)=2\csc(2θ)
verificar csc^4(x)-cot^4(x)=2cot^2(x)+1	prove\:\csc^{4}(x)-\cot^{4}(x)=2\cot^{2}(x)+1
verificar cos(-x)-sin(-x)=cos(x)+sin(x)	prove\:\cos(-x)-\sin(-x)=\cos(x)+\sin(x)
verificar cos(θ)sec(θ)=1	prove\:\cos(θ)\sec(θ)=1
verificar cos(a+b)+cos(a-b)=2cos(a)cos(b)	prove\:\cos(a+b)+\cos(a-b)=2\cos(a)\cos(b)
verificar csc^2(x)-cos^2(x)csc^2(x)=1	prove\:\csc^{2}(x)-\cos^{2}(x)\csc^{2}(x)=1
verificar tan(pi/2-u)=cot(u)	prove\:\tan(\frac{π}{2}-u)=\cot(u)
verificar csc(θ)-cot(θ)=(sin(θ))/(1+cos(θ))	prove\:\csc(θ)-\cot(θ)=\frac{\sin(θ)}{1+\cos(θ)}
verificar tan(2pi-θ)=-tan(θ)	prove\:\tan(2π-θ)=-\tan(θ)
verificar sin^4(θ)-cos^4(θ)=1-2cos^2(θ)	prove\:\sin^{4}(θ)-\cos^{4}(θ)=1-2\cos^{2}(θ)
verificar (1+tan(x))/(1-tan(x))+(1+cot(x))/(1-cot(x))=0	prove\:\frac{1+\tan(x)}{1-\tan(x)}+\frac{1+\cot(x)}{1-\cot(x)}=0
verificar cos(4x)=1-8sin^2(x)cos^2(x)	prove\:\cos(4x)=1-8\sin^{2}(x)\cos^{2}(x)
verificar (sin(x))/(1-cos(-x))=csc(x)+cot(x)	prove\:\frac{\sin(x)}{1-\cos(-x)}=\csc(x)+\cot(x)
verificar tan(x)-tan(y)=(sin(x-y))/(cos(x)cos(y))	prove\:\tan(x)-\tan(y)=\frac{\sin(x-y)}{\cos(x)\cos(y)}
verificar 1+cos(2x)+2sin^2(x)=2	prove\:1+\cos(2x)+2\sin^{2}(x)=2
verificar 1/(tan(x)+cot(x))=sin(x)cos(x)	prove\:\frac{1}{\tan(x)+\cot(x)}=\sin(x)\cos(x)
verificar tan^3(x)=tan(x)sec^2(x)-tan(x)	prove\:\tan^{3}(x)=\tan(x)\sec^{2}(x)-\tan(x)
verificar cos(θ)(sec(θ)-cos(θ))=sin^2(θ)	prove\:\cos(θ)(\sec(θ)-\cos(θ))=\sin^{2}(θ)
verificar (2cot(x))/(csc^2(x))=sin(2x)	prove\:\frac{2\cot(x)}{\csc^{2}(x)}=\sin(2x)
verificar cos^4(x)-sin^4(x)=2cos^2(x)-1	prove\:\cos^{4}(x)-\sin^{4}(x)=2\cos^{2}(x)-1
verificar tan(x)(cot(x)+tan(x))=sec^2(x)	prove\:\tan(x)(\cot(x)+\tan(x))=\sec^{2}(x)
verificar (1+sin(2x))/(sin(2x))=1+1/2 sec(x)csc(x)	prove\:\frac{1+\sin(2x)}{\sin(2x)}=1+\frac{1}{2}\sec(x)\csc(x)
verificar 1/(csc(x)+1)+1/(sin(x)+1)=1	prove\:\frac{1}{\csc(x)+1}+\frac{1}{\sin(x)+1}=1
verificar cos(2u)=cos^2(u)-sin^2(u)	prove\:\cos(2u)=\cos^{2}(u)-\sin^{2}(u)
verificar (csc(θ)+1)(csc(θ)-1)=cot^2(θ)	prove\:(\csc(θ)+1)(\csc(θ)-1)=\cot^{2}(θ)
verificar cos(θ)(cot(θ)+tan(θ))=csc(θ)	prove\:\cos(θ)(\cot(θ)+\tan(θ))=\csc(θ)
verificar sin(-θ)=-sin(θ)	prove\:\sin(-θ)=-\sin(θ)
verificar-sin(x)=sin(-x)	prove\:-\sin(x)=\sin(-x)
verificar (sin(y)+tan(y))/(1+sec(y))=sin(y)	prove\:\frac{\sin(y)+\tan(y)}{1+\sec(y)}=\sin(y)
verificar cos^2(2x)-sin^2(2x)=cos(4x)	prove\:\cos^{2}(2x)-\sin^{2}(2x)=\cos(4x)
verificar (sec^2(x)-1)/(sin(x))=(sin(x))/(1-sin^2(x))	prove\:\frac{\sec^{2}(x)-1}{\sin(x)}=\frac{\sin(x)}{1-\sin^{2}(x)}
verificar sin(pi/4+x)+sin(pi/4-x)=sqrt(2)cos(x)	prove\:\sin(\frac{π}{4}+x)+\sin(\frac{π}{4}-x)=\sqrt{2}\cos(x)
verificar sin(θ)sec(θ)cot(θ)=1	prove\:\sin(θ)\sec(θ)\cot(θ)=1
verificar 1+sec^2(θ)sin^2(θ)=sec^2(θ)	prove\:1+\sec^{2}(θ)\sin^{2}(θ)=\sec^{2}(θ)
verificar 3sin^2(x)+4cos^2(x)=3+cos^2(x)	prove\:3\sin^{2}(x)+4\cos^{2}(x)=3+\cos^{2}(x)
verificar tan(pi/2-θ)tan(θ)=1	prove\:\tan(\frac{π}{2}-θ)\tan(θ)=1
verificar (1-sin^2(x))csc^2(x)=cot^2(x)	prove\:(1-\sin^{2}(x))\csc^{2}(x)=\cot^{2}(x)

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