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Problemas populares de Trigonometría

verificar tan(8θ)-tan(8θ)tan^2(4θ)=2tan(4θ)	prove\:\tan(8θ)-\tan(8θ)\tan^{2}(4θ)=2\tan(4θ)
verificar sec(x)=(cot(x)+tan(x))/(csc(x))	prove\:\sec(x)=\frac{\cot(x)+\tan(x)}{\csc(x)}
verificar (tan(x)+cot(x))^2=sec^2(x)csc^2(x)	prove\:(\tan(x)+\cot(x))^{2}=\sec^{2}(x)\csc^{2}(x)
verificar cot^2(x)+csc^2(x)=2csc^2(x)-1	prove\:\cot^{2}(x)+\csc^{2}(x)=2\csc^{2}(x)-1
verificar (1+tan^2(x))(1-sin^2(x))=1	prove\:(1+\tan^{2}(x))(1-\sin^{2}(x))=1
verificar (cos(θ))/(1-sin(θ))=(sin(θ)-csc(θ))/(cos(θ)-cot(θ))	prove\:\frac{\cos(θ)}{1-\sin(θ)}=\frac{\sin(θ)-\csc(θ)}{\cos(θ)-\cot(θ)}
verificar csc^2(x)= 1/(sin^2(x))	prove\:\csc^{2}(x)=\frac{1}{\sin^{2}(x)}
verificar (sec^2(θ)-1)cos^2(θ)=sin^2(θ)	prove\:(\sec^{2}(θ)-1)\cos^{2}(θ)=\sin^{2}(θ)
verificar (sin(θ)+tan(θ))/(1+cos(θ))=tan(θ)	prove\:\frac{\sin(θ)+\tan(θ)}{1+\cos(θ)}=\tan(θ)
verificar cos^2(β)-sin^2(β)=2cos^2(β)-1	prove\:\cos^{2}(β)-\sin^{2}(β)=2\cos^{2}(β)-1
verificar (1-cos(β))(1+cos(β))= 1/(csc^2(β))	prove\:(1-\cos(β))(1+\cos(β))=\frac{1}{\csc^{2}(β)}
verificar (cot(θ)sec(θ))/(csc(θ))=1	prove\:\frac{\cot(θ)\sec(θ)}{\csc(θ)}=1
verificar sin(θ)csc(θ)-cos^2(θ)=sin^2(θ)	prove\:\sin(θ)\csc(θ)-\cos^{2}(θ)=\sin^{2}(θ)
verificar tan^2(θ)+1= 1/(cos^2(θ))	prove\:\tan^{2}(θ)+1=\frac{1}{\cos^{2}(θ)}
verificar 1/(1+tan^2(x))=cos^2(x)	prove\:\frac{1}{1+\tan^{2}(x)}=\cos^{2}(x)
verificar (2tan(x))/(sec^2(x))=sin(2x)	prove\:\frac{2\tan(x)}{\sec^{2}(x)}=\sin(2x)
verificar csc^2(x)-1=cot^2(x)	prove\:\csc^{2}(x)-1=\cot^{2}(x)
verificar sin^2(x)cos(x)sec(x)=1-cos^2(x)	prove\:\sin^{2}(x)\cos(x)\sec(x)=1-\cos^{2}(x)
verificar tan^2(x)cos^2(x)=1-cos^2(x)	prove\:\tan^{2}(x)\cos^{2}(x)=1-\cos^{2}(x)
verificar 2csc(2θ)cos(2θ)=cot(θ)-tan(θ)	prove\:2\csc(2θ)\cos(2θ)=\cot(θ)-\tan(θ)
verificar 6sin(x)cos(x)=3sin(2x)	prove\:6\sin(x)\cos(x)=3\sin(2x)
verificar (tan^2(θ))/(sec(θ))=sin(θ)tan(θ)	prove\:\frac{\tan^{2}(θ)}{\sec(θ)}=\sin(θ)\tan(θ)
verificar sin(x)+cos(x)=(1+tan(x))/(sec(x))	prove\:\sin(x)+\cos(x)=\frac{1+\tan(x)}{\sec(x)}
verificar (tan^2(θ))/(sec(θ))=sec(θ)-cos(θ)	prove\:\frac{\tan^{2}(θ)}{\sec(θ)}=\sec(θ)-\cos(θ)
verificar (cos^2(θ))/(1-sin(θ))=1+sin(θ)	prove\:\frac{\cos^{2}(θ)}{1-\sin(θ)}=1+\sin(θ)
verificar 2csc(2x)=tan(x)+cot(x)	prove\:2\csc(2x)=\tan(x)+\cot(x)
verificar cos(x+y)=cos(x)cos(y)-sin(x)sin(y)	prove\:\cos(x+y)=\cos(x)\cos(y)-\sin(x)\sin(y)
verificar sec^2(x)=tan^2(x)+1	prove\:\sec^{2}(x)=\tan^{2}(x)+1
verificar (1-cos(θ))/(sin(θ))=csc(θ)-cot(θ)	prove\:\frac{1-\cos(θ)}{\sin(θ)}=\csc(θ)-\cot(θ)
verificar csc^2(x)(1-sin^2(x))=cot^2(x)	prove\:\csc^{2}(x)(1-\sin^{2}(x))=\cot^{2}(x)
verificar sin(3x)=(sin(x))(4cos^2(x)-1)	prove\:\sin(3x)=(\sin(x))(4\cos^{2}(x)-1)
verificar sin(2a)=2sin(a)cos(a)	prove\:\sin(2a)=2\sin(a)\cos(a)
verificar tan(x+pi/2)=-cot(x)	prove\:\tan(x+\frac{π}{2})=-\cot(x)
verificar cos(θ)tan(θ)csc(θ)=1	prove\:\cos(θ)\tan(θ)\csc(θ)=1
verificar csc(x)+cot(x)= 1/(csc(x)-cot(x))	prove\:\csc(x)+\cot(x)=\frac{1}{\csc(x)-\cot(x)}
verificar 1-sin^2(x)=cos^2(x)	prove\:1-\sin^{2}(x)=\cos^{2}(x)
verificar (cos(pi-x))/(cos(pi/2+x))=cot(x)	prove\:\frac{\cos(π-x)}{\cos(\frac{π}{2}+x)}=\cot(x)
verificar cos^2(x)(sec(x)+1)^2=(1+cos(x))^2	prove\:\cos^{2}(x)(\sec(x)+1)^{2}=(1+\cos(x))^{2}
verificar cot^2(x)cos^2(x)=cot^2(x)-cos^2(x)	prove\:\cot^{2}(x)\cos^{2}(x)=\cot^{2}(x)-\cos^{2}(x)
verificar sin(a)=cos(90+a)	prove\:\sin(a)=\cos(90^{\circ\:}+a)
verificar cot(θ)+tan(θ)=2csc(2θ)	prove\:\cot(θ)+\tan(θ)=2\csc(2θ)
verificar tan^2(a)-sin^2(a)=tan^2(a)sin^2(a)	prove\:\tan^{2}(a)-\sin^{2}(a)=\tan^{2}(a)\sin^{2}(a)
verificar cos(x)(tan(x)-sec(-x))=sin(x)-1	prove\:\cos(x)(\tan(x)-\sec(-x))=\sin(x)-1
verificar 1-2sin^2(x)=2cos^2(x)-1	prove\:1-2\sin^{2}(x)=2\cos^{2}(x)-1
verificar cot(u)-csc(u)=-(sin(u))/(1+cos(u))	prove\:\cot(u)-\csc(u)=-\frac{\sin(u)}{1+\cos(u)}
verificar sec^2(θ)-tan^2(θ)=1	prove\:\sec^{2}(θ)-\tan^{2}(θ)=1
verificar (1+tan^2(x))/(tan^2(x))=csc^2(x)	prove\:\frac{1+\tan^{2}(x)}{\tan^{2}(x)}=\csc^{2}(x)
verificar 1/(sec^2(x))+1/(csc^2(x))=1	prove\:\frac{1}{\sec^{2}(x)}+\frac{1}{\csc^{2}(x)}=1
verificar (1+tan^2(x))cot^2(x)=csc^2(x)	prove\:(1+\tan^{2}(x))\cot^{2}(x)=\csc^{2}(x)
verificar csc(θ)sec(θ)-cot(θ)=tan(θ)	prove\:\csc(θ)\sec(θ)-\cot(θ)=\tan(θ)
verificar 1-tan^2(θ/2)=(2cos(θ))/(1+cos(θ))	prove\:1-\tan^{2}(\frac{θ}{2})=\frac{2\cos(θ)}{1+\cos(θ)}
verificar sin(x+y)sec(x)sec(y)=tan(x)+tan(y)	prove\:\sin(x+y)\sec(x)\sec(y)=\tan(x)+\tan(y)
verificar (sin(x)-csc(x))/(csc(x))=-cos^2(x)	prove\:\frac{\sin(x)-\csc(x)}{\csc(x)}=-\cos^{2}(x)
verificar (cos(x))/(1-sin^2(x))=sec(x)	prove\:\frac{\cos(x)}{1-\sin^{2}(x)}=\sec(x)
verificar tan(2x)-2tan(2x)sin^2(x)=sin(2x)	prove\:\tan(2x)-2\tan(2x)\sin^{2}(x)=\sin(2x)
verificar cot^2(θ)csc^2(θ)-cot^2(θ)=cot^4(θ)	prove\:\cot^{2}(θ)\csc^{2}(θ)-\cot^{2}(θ)=\cot^{4}(θ)
verificar sin(x-pi)=-sin(x)	prove\:\sin(x-π)=-\sin(x)
verificar cos^2(x)+tan^2(x)cos^2(x)=1	prove\:\cos^{2}(x)+\tan^{2}(x)\cos^{2}(x)=1
verificar sec^2(x)-1=tan^2(x)	prove\:\sec^{2}(x)-1=\tan^{2}(x)
verificar cos(x-pi/3)+sin(pi/6-x)=cos(x)	prove\:\cos(x-\frac{π}{3})+\sin(\frac{π}{6}-x)=\cos(x)
verificar coth^2(x)-1=csch^2(x)	prove\:\coth^{2}(x)-1=\csch^{2}(x)
verificar (cos^4(x)-sin^4(x))/(cos^2(x))=1-tan^2(x)	prove\:\frac{\cos^{4}(x)-\sin^{4}(x)}{\cos^{2}(x)}=1-\tan^{2}(x)
verificar csc^2(x)+cot^2(x)=2csc^2(x)-1	prove\:\csc^{2}(x)+\cot^{2}(x)=2\csc^{2}(x)-1
verificar cot(pi/2-x)=tan(x)	prove\:\cot(\frac{π}{2}-x)=\tan(x)
verificar (1-cos^2(x))/(sin(x))=sin(x)	prove\:\frac{1-\cos^{2}(x)}{\sin(x)}=\sin(x)
verificar csc^2(x)=1+cot^2(x)	prove\:\csc^{2}(x)=1+\cot^{2}(x)
verificar cot^2(x)-csc^2(x)=-1	prove\:\cot^{2}(x)-\csc^{2}(x)=-1
verificar 1/(cos^2(x))=sec^2(x)	prove\:\frac{1}{\cos^{2}(x)}=\sec^{2}(x)
verificar cot(a)sec(a)=csc(a)	prove\:\cot(a)\sec(a)=\csc(a)
verificar sec^2(θ)+csc^2(θ)=sec^2(θ)csc^2(θ)	prove\:\sec^{2}(θ)+\csc^{2}(θ)=\sec^{2}(θ)\csc^{2}(θ)
verificar tan(x/2)+cot(x/2)=2csc(x)	prove\:\tan(\frac{x}{2})+\cot(\frac{x}{2})=2\csc(x)
verificar sec(x)-tan(x)=(1-sin(x))/(cos(x))	prove\:\sec(x)-\tan(x)=\frac{1-\sin(x)}{\cos(x)}
verificar sin((3pi)/2+x)=-cos(x)	prove\:\sin(\frac{3π}{2}+x)=-\cos(x)
verificar (cos^2(t))/(sin(t))=csc(t)-sin(t)	prove\:\frac{\cos^{2}(t)}{\sin(t)}=\csc(t)-\sin(t)
verificar sin(x)tan(x)=(1-cos^2(x))/(cos(x))	prove\:\sin(x)\tan(x)=\frac{1-\cos^{2}(x)}{\cos(x)}
verificar sec(u)+tan(u)=(cos(u))/(1-sin(u))	prove\:\sec(u)+\tan(u)=\frac{\cos(u)}{1-\sin(u)}
verificar cos(x-pi/6)-cos(x+pi/6)=sin(x)	prove\:\cos(x-\frac{π}{6})-\cos(x+\frac{π}{6})=\sin(x)
verificar cos((3pi)/2+θ)=sin(θ)	prove\:\cos(\frac{3π}{2}+θ)=\sin(θ)
verificar csc^2(θ)-cos^2(θ)csc^2(θ)=1	prove\:\csc^{2}(θ)-\cos^{2}(θ)\csc^{2}(θ)=1
verificar tan(2θ)=(2tan(θ))/(1-tan^2(θ))	prove\:\tan(2θ)=\frac{2\tan(θ)}{1-\tan^{2}(θ)}
verificar sin^2(θ)tan^2(θ)=tan^2(θ)-sin^2(θ)	prove\:\sin^{2}(θ)\tan^{2}(θ)=\tan^{2}(θ)-\sin^{2}(θ)
verificar 1-tan^2(x)=2-sec^2(x)	prove\:1-\tan^{2}(x)=2-\sec^{2}(x)
verificar sin^2(x)+2cos^2(x)=2-sin^2(x)	prove\:\sin^{2}(x)+2\cos^{2}(x)=2-\sin^{2}(x)
verificar (csc(x)+cot(x))(csc(x)-cot(x))=1	prove\:(\csc(x)+\cot(x))(\csc(x)-\cot(x))=1
verificar cot^2(θ)-csc^2(θ)=-1	prove\:\cot^{2}(θ)-\csc^{2}(θ)=-1
verificar (sec^2(t)-1)/(sec^2(t))=sin^2(t)	prove\:\frac{\sec^{2}(t)-1}{\sec^{2}(t)}=\sin^{2}(t)
verificar cos(θ)=cos(-θ)	prove\:\cos(θ)=\cos(-θ)
verificar 4cos^3(x)-3cos(x)=cos(3x)	prove\:4\cos^{3}(x)-3\cos(x)=\cos(3x)
verificar (csc^2(θ))/(cot(θ))=sec(θ)csc(θ)	prove\:\frac{\csc^{2}(θ)}{\cot(θ)}=\sec(θ)\csc(θ)
verificar tan(θ)cot(θ)-cos^2(θ)=sin^2(θ)	prove\:\tan(θ)\cot(θ)-\cos^{2}(θ)=\sin^{2}(θ)
verificar (cot^2(x))/(csc(x)+1)=csc(x)-1	prove\:\frac{\cot^{2}(x)}{\csc(x)+1}=\csc(x)-1
verificar csc^2(-θ)-1=cot^2(θ)	prove\:\csc^{2}(-θ)-1=\cot^{2}(θ)
verificar ((sec(θ)-tan(θ))^2+1)/(sec(θ)csc(θ)-tan(θ)csc(θ))=2tan(θ)	prove\:\frac{(\sec(θ)-\tan(θ))^{2}+1}{\sec(θ)\csc(θ)-\tan(θ)\csc(θ)}=2\tan(θ)
verificar 1/(csc(x)-cot(x))=csc(x)+cot(x)	prove\:\frac{1}{\csc(x)-\cot(x)}=\csc(x)+\cot(x)
verificar (sec(x)+tan(x))(sec(x)-tan(x))=1	prove\:(\sec(x)+\tan(x))(\sec(x)-\tan(x))=1
verificar csc(x)(sin(x)+cos(x))=1+cot(x)	prove\:\csc(x)(\sin(x)+\cos(x))=1+\cot(x)
verificar (1-cos^2(x))cot^2(x)=cos^2(x)	prove\:(1-\cos^{2}(x))\cot^{2}(x)=\cos^{2}(x)
verificar cos(6x)=2cos^2(3x)-1	prove\:\cos(6x)=2\cos^{2}(3x)-1
verificar tan^2(x)-tan^2(x)sin^2(x)=sin^2(x)	prove\:\tan^{2}(x)-\tan^{2}(x)\sin^{2}(x)=\sin^{2}(x)
verificar (1-sin^2(x))/(cos(x))=cos(x)	prove\:\frac{1-\sin^{2}(x)}{\cos(x)}=\cos(x)

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