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Problemas populares de Trigonometría

verificar cos^2(x)=(1-sin(x))(1+sin(x))	prove\:\cos^{2}(x)=(1-\sin(x))(1+\sin(x))
verificar cot(θ)(tan(θ)+cot(θ))=csc^2(θ)	prove\:\cot(θ)(\tan(θ)+\cot(θ))=\csc^{2}(θ)
verificar csc(θ)-cot(θ)cos(θ)=sin(θ)	prove\:\csc(θ)-\cot(θ)\cos(θ)=\sin(θ)
verificar 2cos(3((11pi)/(12)))=-sqrt(2)	prove\:2\cos(3(\frac{11π}{12}))=-\sqrt{2}
verificar sin(θ)+sin(θ)cot^2(θ)=csc(θ)	prove\:\sin(θ)+\sin(θ)\cot^{2}(θ)=\csc(θ)
verificar ((cos(x)sec(x)))/(tan(x))=cot(x)	prove\:\frac{(\cos(x)\sec(x))}{\tan(x)}=\cot(x)
verificar+sin(z+w)=sin(z)cos(w)+cos(z)sin(w)	prove\:+\sin(z+w)=\sin(z)\cos(w)+\cos(z)\sin(w)
verificar (sin^2(x)+cos^2(x))^5=1	prove\:(\sin^{2}(x)+\cos^{2}(x))^{5}=1
verificar (cot^2(x)-1)/(2cot(x))=cot(2x)	prove\:\frac{\cot^{2}(x)-1}{2\cot(x)}=\cot(2x)
verificar csc(θ)=(sec(θ))/(tan(θ))	prove\:\csc(θ)=\frac{\sec(θ)}{\tan(θ)}
verificar tan^2(B)-sin^2(B)=tan^2(B)sin^2(B)	prove\:\tan^{2}(B)-\sin^{2}(B)=\tan^{2}(B)\sin^{2}(B)
verificar (cos(2x)+1)/(sin(2x))=cot(x)	prove\:\frac{\cos(2x)+1}{\sin(2x)}=\cot(x)
verificar cos(x)+2sin^2(x/2)=1	prove\:\cos(x)+2\sin^{2}(\frac{x}{2})=1
verificar-tan(t)-(cos(t))/(sin(t)-1)=sec(x)	prove\:-\tan(t)-\frac{\cos(t)}{\sin(t)-1}=\sec(x)
verificar (cot(x))/(tan(x)sec(x))=csc(x)-1	prove\:\frac{\cot(x)}{\tan(x)\sec(x)}=\csc(x)-1
verificar cos(x/2)=sqrt(((1+cos(x)))/2)	prove\:\cos(\frac{x}{2})=\sqrt{\frac{(1+\cos(x))}{2}}
verificar sin^2(x)-(cos(x)sin(x))/(tan(x))=1	prove\:\sin^{2}(x)-\frac{\cos(x)\sin(x)}{\tan(x)}=1
verificar tan^2(A)+1=sec^2(A)	prove\:\tan^{2}(A)+1=\sec^{2}(A)
verificar (tan(x)+1)/(sec(x))=sin(x)+cos(x)	prove\:\frac{\tan(x)+1}{\sec(x)}=\sin(x)+\cos(x)
verificar cos(pi/2-x)cot(x)=cos(x)	prove\:\cos(\frac{π}{2}-x)\cot(x)=\cos(x)
verificar (cos(x))/(sin^2(x))=cot(x)csc(x)	prove\:\frac{\cos(x)}{\sin^{2}(x)}=\cot(x)\csc(x)
verificar 2sin(9pi-x)=2sin(x)	prove\:2\sin(9π-x)=2\sin(x)
verificar 1csc(θ)-sin(θ)=cot(θ)cos(θ)	prove\:1\csc(θ)-\sin(θ)=\cot(θ)\cos(θ)
verificar (sec(x))/(csc^2(x))=sec(x)-cos(x)	prove\:\frac{\sec(x)}{\csc^{2}(x)}=\sec(x)-\cos(x)
verificar 1/(sin(θ)+1)=(1-sin(θ))/(cos^2(θ))	prove\:\frac{1}{\sin(θ)+1}=\frac{1-\sin(θ)}{\cos^{2}(θ)}
verificar sin(x)cos(x)tan(x)cot(x)=1	prove\:\sin(x)\cos(x)\tan(x)\cot(x)=1
verificar (1-cos(x))=cos(x)-1	prove\:(1-\cos(x))=\cos(x)-1
verificar cos^2(x)=1+cos(2x)	prove\:\cos^{2}(x)=1+\cos(2x)
verificar sin(θ-pi/2)+sin(θ+pi/2)=0	prove\:\sin(θ-\frac{π}{2})+\sin(θ+\frac{π}{2})=0
verificar 1=cos^2(x)+sin^2(x)	prove\:1=\cos^{2}(x)+\sin^{2}(x)
verificar (cos^2(x))/(csc^2(x)-1)=sin^2(x)	prove\:\frac{\cos^{2}(x)}{\csc^{2}(x)-1}=\sin^{2}(x)
verificar (sin^2(x)+cos^2(x))^3=1	prove\:(\sin^{2}(x)+\cos^{2}(x))^{3}=1
verificar sec^4(x)-1=2tan^2(x)+tan^4(x)	prove\:\sec^{4}(x)-1=2\tan^{2}(x)+\tan^{4}(x)
verificar tan^2(x)+1= 1/(cot^2(x))+1	prove\:\tan^{2}(x)+1=\frac{1}{\cot^{2}(x)}+1
verificar sec(pi/4+x)sec(pi/4-x)=2sec(2x)	prove\:\sec(\frac{π}{4}+x)\sec(\frac{π}{4}-x)=2\sec(2x)
verificar cot(x)sec(x)(1-cos^2(x))=sin(x)	prove\:\cot(x)\sec(x)(1-\cos^{2}(x))=\sin(x)
verificar tan(x)+2=2+sec(x)sin(x)	prove\:\tan(x)+2=2+\sec(x)\sin(x)
verificar 2sin^3(x)cos(x)+2sin(x)cos^3(x)=sin(2x)	prove\:2\sin^{3}(x)\cos(x)+2\sin(x)\cos^{3}(x)=\sin(2x)
verificar tan^2(α)(1-sin^2(α))=sin^2(α)	prove\:\tan^{2}(α)(1-\sin^{2}(α))=\sin^{2}(α)
verificar (1-sin^2(θ))/(sin^2(θ))=cot^2(θ)	prove\:\frac{1-\sin^{2}(θ)}{\sin^{2}(θ)}=\cot^{2}(θ)
verificar sin(x)=tan(x)cos(x)	prove\:\sin(x)=\tan(x)\cos(x)
verificar sin(θ)*(cot(θ)+tan(θ))=sec(θ)	prove\:\sin(θ)\cdot\:(\cot(θ)+\tan(θ))=\sec(θ)
verificar tan(x)+10=(sin(x)+10)/(cos(x))	prove\:\tan(x)+10=\frac{\sin(x)+10}{\cos(x)}
verificar ((sin^2(t)))/(tan^2(t))=cos^2(t)	prove\:\frac{(\sin^{2}(t))}{\tan^{2}(t)}=\cos^{2}(t)
verificar sin(A)sec(A)=tan(A)	prove\:\sin(A)\sec(A)=\tan(A)
verificar csc(x)tan(x)cos(x)=1	prove\:\csc(x)\tan(x)\cos(x)=1
verificar tan^2(x/2)+2tan(x/2)-5=3tan(x/2)	prove\:\tan^{2}(\frac{x}{2})+2\tan(\frac{x}{2})-5=3\tan(\frac{x}{2})
verificar 3(sec(θ)-tan(θ))(csc(θ)+1)=3cot(θ)	prove\:3(\sec(θ)-\tan(θ))(\csc(θ)+1)=3\cot(θ)
verificar (sin(x))/(cos^2(x))=tan(x)sec(x)	prove\:\frac{\sin(x)}{\cos^{2}(x)}=\tan(x)\sec(x)
verificar (cot(x)+2)/(csc(x))=2sin(x)+cos(x)	prove\:\frac{\cot(x)+2}{\csc(x)}=2\sin(x)+\cos(x)
verificar (sec(x))(sin(x))=tan(x)	prove\:(\sec(x))(\sin(x))=\tan(x)
verificar tan(2x)=2sin(x)cos(x)sec(2x)	prove\:\tan(2x)=2\sin(x)\cos(x)\sec(2x)
verificar sin^3(z)cos^2(z)=sin^3(z)-sin^5(z)	prove\:\sin^{3}(z)\cos^{2}(z)=\sin^{3}(z)-\sin^{5}(z)
verificar (cos(x)sec(x))/(cot(x)tan(x))=1	prove\:\frac{\cos(x)\sec(x)}{\cot(x)\tan(x)}=1
verificar sec(x)=sin(x)*(tan(x)+cot(x))	prove\:\sec(x)=\sin(x)\cdot\:(\tan(x)+\cot(x))
verificar 8cos^4(x)-8sin^4(x)=8cos(2x)	prove\:8\cos^{4}(x)-8\sin^{4}(x)=8\cos(2x)
verificar (cot(θ)+tan(θ))sin(θ)=sec(θ)	prove\:(\cot(θ)+\tan(θ))\sin(θ)=\sec(θ)
verificar tan(x)csc(x)= 1/(cos(x))	prove\:\tan(x)\csc(x)=\frac{1}{\cos(x)}
verificar cos(A)=2cos(A)sin(B)	prove\:\cos(A)=2\cos(A)\sin(B)
verificar cos(180-θ)=-cos(θ)	prove\:\cos(180^{\circ\:}-θ)=-\cos(θ)
verificar cos^3(x)=(1-sin^2(x))(cos(x))	prove\:\cos^{3}(x)=(1-\sin^{2}(x))(\cos(x))
verificar tan(3x)cos(3x)=sin(3x)	prove\:\tan(3x)\cos(3x)=\sin(3x)
verificar 1-2sin(θ)cos(θ)=(cos(θ)-sin(θ))^2	prove\:1-2\sin(θ)\cos(θ)=(\cos(θ)-\sin(θ))^{2}
verificar 5cos(x)+5sin(x)tan(x)=5sec(x)	prove\:5\cos(x)+5\sin(x)\tan(x)=5\sec(x)
verificar 9cos^2(x)-9sin^2(x)=9-18sin^2(x)	prove\:9\cos^{2}(x)-9\sin^{2}(x)=9-18\sin^{2}(x)
verificar cos^2(x)tan^2(x)csc(x)=sin(x)	prove\:\cos^{2}(x)\tan^{2}(x)\csc(x)=\sin(x)
verificar 7cos^2(B)-7sin^2(B)=14cos^2(B)-7	prove\:7\cos^{2}(B)-7\sin^{2}(B)=14\cos^{2}(B)-7
verificar sec^2(x)(sec(x)-cos(x))=tan^2(x)	prove\:\sec^{2}(x)(\sec(x)-\cos(x))=\tan^{2}(x)
verificar sin^2(x)tan(x)=tan(x)-cos(x)sin(x)	prove\:\sin^{2}(x)\tan(x)=\tan(x)-\cos(x)\sin(x)
verificar 1-(sin(x))/(1+cos(x))=cos(x)	prove\:1-\frac{\sin(x)}{1+\cos(x)}=\cos(x)
verificar 2cos(3x)=cot(3x)	prove\:2\cos(3x)=\cot(3x)
verificar cos^2(θ)tan^2(θ)+cos^2(θ)=1	prove\:\cos^{2}(θ)\tan^{2}(θ)+\cos^{2}(θ)=1
verificar (sin(θ)csc(θ))/(tan(θ))=cot(θ)	prove\:\frac{\sin(θ)\csc(θ)}{\tan(θ)}=\cot(θ)
verificar sec^2(θ)+csc(θ)=-sec^2(θ)csc(θ)	prove\:\sec^{2}(θ)+\csc(θ)=-\sec^{2}(θ)\csc(θ)
verificar tan(5x)=tan(3x)sec(2x)-tan(3x)	prove\:\tan(5x)=\tan(3x)\sec(2x)-\tan(3x)
verificar 1-2cos^2(x)=sin^2(x)-cos^2(x)	prove\:1-2\cos^{2}(x)=\sin^{2}(x)-\cos^{2}(x)
verificar sin(40)=2sin(20)cos(20)	prove\:\sin(40^{\circ\:})=2\cdot\:\sin(20^{\circ\:})\cdot\:\cos(20^{\circ\:})
verificar 9sec(y)cos(y)=9	prove\:9\sec(y)\cos(y)=9
verificar-sin(-x)=sin(x)	prove\:-\sin(-x)=\sin(x)
verificar (tan(x)-sec(x))(sin(x)+1)=-cos(x)	prove\:(\tan(x)-\sec(x))(\sin(x)+1)=-\cos(x)
verificar tan^2(x)+2=sec^2(x)+1	prove\:\tan^{2}(x)+2=\sec^{2}(x)+1
verificar csc(x)+sec(x)=tan(x)	prove\:\csc(x)+\sec(x)=\tan(x)
verificar (sin^2(x))/(sec^2(x)-1)=cos^2(x)	prove\:\frac{\sin^{2}(x)}{\sec^{2}(x)-1}=\cos^{2}(x)
verificar tan^2(x)+1=2	prove\:\tan^{2}(x)+1=2
verificar tan^2(t)sin^2(t)=tan^2(t)-sin^2(t)	prove\:\tan^{2}(t)\sin^{2}(t)=\tan^{2}(t)-\sin^{2}(t)
verificar 8sin^2(θ)+9cos^2(θ)=8+cos^2(θ)	prove\:8\sin^{2}(θ)+9\cos^{2}(θ)=8+\cos^{2}(θ)
verificar 2=cos^4(+sin^4(x))	prove\:2=\cos^{4}(+\sin^{4}(x))
verificar sec^2(x)+tan^2(x)=1+2tan^2(x)	prove\:\sec^{2}(x)+\tan^{2}(x)=1+2\tan^{2}(x)
verificar (sin(a+b))/(sin(a-b))=(1+cot(a)tan(b))/(1-cot(a)tan(b))	prove\:\frac{\sin(a+b)}{\sin(a-b)}=\frac{1+\cot(a)\tan(b)}{1-\cot(a)\tan(b)}
verificar cot(x+pi)=cot(x)	prove\:\cot(x+π)=\cot(x)
verificar (cos(x)+tan(x))^2=csc^2(x)sec^2(x)	prove\:(\cos(x)+\tan(x))^{2}=\csc^{2}(x)\sec^{2}(x)
verificar tan(x)(2-cos(x))^2=0	prove\:\tan(x)(2-\cos(x))^{2}=0
verificar 2cos(a)-sin(2a)csc(a)=0	prove\:2\cos(a)-\sin(2a)\csc(a)=0
verificar sin(A)=csc(A)tan(A)	prove\:\sin(A)=\csc(A)\tan(A)
verificar sec(A)csc(A)=sec(A)cot(A)	prove\:\sec(A)\csc(A)=\sec(A)\cot(A)
verificar 1-2sin^2(x)=-1+2cos^2(x)	prove\:1-2\sin^{2}(x)=-1+2\cos^{2}(x)
verificar 1/(cos(x))-sin(x)tan(x)=cos(x)	prove\:\frac{1}{\cos(x)}-\sin(x)\tan(x)=\cos(x)
verificar (cos(5x)+cos(3x))/(sin(5x)+sin(3x))=cot(4x)	prove\:\frac{\cos(5x)+\cos(3x)}{\sin(5x)+\sin(3x)}=\cot(4x)
verificar cos^2(x/2)=(1+cos(x))/2	prove\:\cos^{2}(\frac{x}{2})=\frac{1+\cos(x)}{2}
verificar (sin(x)+cos(x))/(sin(x))=1+cot(x)	prove\:\frac{\sin(x)+\cos(x)}{\sin(x)}=1+\cot(x)

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