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Problemas populares de Trigonometría

verificar cos(θ)sec(pi/2-θ)=cot(θ)	prove\:\cos(θ)\sec(\frac{π}{2}-θ)=\cot(θ)
verificar 4cos^4(x)-4sin^4(x)=4cos(2x)	prove\:4\cos^{4}(x)-4\sin^{4}(x)=4\cos(2x)
verificar csc(x)(1+sin(x))=1+csc(x)	prove\:\csc(x)(1+\sin(x))=1+\csc(x)
verificar sin(x+y)sin(x-y)=sin(2x)-sin(2y)	prove\:\sin(x+y)\sin(x-y)=\sin(2x)-\sin(2y)
verificar csc^2(x)=1-cot^2(x)	prove\:\csc^{2}(x)=1-\cot^{2}(x)
verificar cos^2(θ)=1+sin^2(θ)	prove\:\cos^{2}(θ)=1+\sin^{2}(θ)
verificar tan^2(x)csc^2(x)=tan^2(x)+1	prove\:\tan^{2}(x)\csc^{2}(x)=\tan^{2}(x)+1
verificar sin((5pi)/6)= 1/2	prove\:\sin(\frac{5π}{6})=\frac{1}{2}
verificar (1+cos(α))(1-cos(α))=sin^2(α)	prove\:(1+\cos(α))(1-\cos(α))=\sin^{2}(α)
verificar tan(pi/2-θ)=cot(θ)	prove\:\tan(\frac{π}{2}-θ)=\cot(θ)
verificar sin^3(x)cos^2(x)=sin^3(x)-sin^5(x)	prove\:\sin^{3}(x)\cos^{2}(x)=\sin^{3}(x)-\sin^{5}(x)
verificar (cos(x)cot(x))/(1-sin(x))=csc(x)	prove\:\frac{\cos(x)\cot(x)}{1-\sin(x)}=\csc(x)
verificar sec(2a)=(csc^2(a))/(cot^2(a)-1)	prove\:\sec(2a)=\frac{\csc^{2}(a)}{\cot^{2}(a)-1}
verificar (2tan(x))/(sin(2x))=1+tan^2(x)	prove\:\frac{2\tan(x)}{\sin(2x)}=1+\tan^{2}(x)
verificar sin(x)=((1-cos(x))/2)^{1/2}	prove\:\sin(x)=(\frac{1-\cos(x)}{2})^{\frac{1}{2}}
verificar sin(0)-1=-1	prove\:\sin(0)-1=-1
verificar sin(θ)cos(θ)cot(θ)+sin^2(θ)=1	prove\:\sin(θ)\cos(θ)\cot(θ)+\sin^{2}(θ)=1
verificar 1+sec(θ)sin(θ)tan(θ)=sec^2(θ)	prove\:1+\sec(θ)\sin(θ)\tan(θ)=\sec^{2}(θ)
verificar (sin(2α))/(1+cos(2α))=tan(α)	prove\:\frac{\sin(2α)}{1+\cos(2α)}=\tan(α)
verificar cos(t)+tan(t)sin(t)=sec(t)	prove\:\cos(t)+\tan(t)\sin(t)=\sec(t)
verificar (1-cos(x))/(-1+1/(cos(x)))=cos(x)	prove\:\frac{1-\cos(x)}{-1+\frac{1}{\cos(x)}}=\cos(x)
verificar cos^4(x)-sin^4(x)=tan^2(x)	prove\:\cos^{4}(x)-\sin^{4}(x)=\tan^{2}(x)
verificar (cos(x)-sin(x))^2=1-2sin(x)*cos(x)	prove\:(\cos(x)-\sin(x))^{2}=1-2\sin(x)\cdot\:\cos(x)
verificar cos(a)=2cos^2(a/2)-1	prove\:\cos(a)=2\cos^{2}(\frac{a}{2})-1
verificar tan^3(x)=(sin^3(x))/(cos^3(x))	prove\:\tan^{3}(x)=\frac{\sin^{3}(x)}{\cos^{3}(x)}
verificar cos(4θ)=1-8sin^2(θ)cos^2(θ)	prove\:\cos(4θ)=1-8\sin^{2}(θ)\cos^{2}(θ)
verificar tan^2(x)-sin^2(x)=(tan(x)sin(x))^2	prove\:\tan^{2}(x)-\sin^{2}(x)=(\tan(x)\sin(x))^{2}
verificar cos^6(105)=((1+cos(210))/2)^3	prove\:\cos^{6}(105^{\circ\:})=(\frac{1+\cos(210^{\circ\:})}{2})^{3}
verificar cos^2(θ)=sin^2(θ)-1	prove\:\cos^{2}(θ)=\sin^{2}(θ)-1
verificar (tan(2θ)+cot(2θ))/(sec(2θ))=csc(2θ)	prove\:\frac{\tan(2θ)+\cot(2θ)}{\sec(2θ)}=\csc(2θ)
verificar (sec(θ))/(sec(θ)-1)= 1/(1-cos(θ))	prove\:\frac{\sec(θ)}{\sec(θ)-1}=\frac{1}{1-\cos(θ)}
verificar 2cos(θ)-(cos(2θ))/(cos(θ))=sec(θ)	prove\:2\cos(θ)-\frac{\cos(2θ)}{\cos(θ)}=\sec(θ)
verificar cos(2*30)=cos^2(30)-sin^2(30)	prove\:\cos(2\cdot\:30)=\cos^{2}(30)-\sin^{2}(30)
verificar 1+tan^2(45)=sec^2(45)	prove\:1+\tan^{2}(45^{\circ\:})=\sec^{2}(45^{\circ\:})
verificar (cot(x))/(cos(x))=csc(x)	prove\:\frac{\cot(x)}{\cos(x)}=\csc(x)
verificar (sin(x)cos(x))/(tan(x))=cos^2(x)	prove\:\frac{\sin(x)\cos(x)}{\tan(x)}=\cos^{2}(x)
verificar 2sin^2(2t)+cos(4t)=1	prove\:2\sin^{2}(2t)+\cos(4t)=1
verificar (cos(θ)+cos(3θ))/(2cos(2θ))=cos(θ)	prove\:\frac{\cos(θ)+\cos(3θ)}{2\cos(2θ)}=\cos(θ)
verificar tan^3(θ)=tan(θ)sec^2(θ)-tan(θ)	prove\:\tan^{3}(θ)=\tan(θ)\sec^{2}(θ)-\tan(θ)
verificar sin^2(θ)+sin(θ)=1	prove\:\sin^{2}(θ)+\sin(θ)=1
verificar 1/(cos^2(x))=1+tan^2(x)	prove\:\frac{1}{\cos^{2}(x)}=1+\tan^{2}(x)
verificar 1/(cos^2(x))=2	prove\:\frac{1}{\cos^{2}(x)}=2
verificar sin(θ-(3pi)/2)=cos(θ)	prove\:\sin(θ-\frac{3π}{2})=\cos(θ)
verificar cos^2(x)+2sin(x)=2	prove\:\cos^{2}(x)+2\sin(x)=2
verificar 2sin^2(x/2)tan(x)=tan(x)-sin(x)	prove\:2\sin^{2}(\frac{x}{2})\tan(x)=\tan(x)-\sin(x)
verificar sin(270+x)=-cos(x)	prove\:\sin(270^{\circ\:}+x)=-\cos(x)
verificar sec^2(x)+csc^2(x)=(csc(x)sec(x))^2	prove\:\sec^{2}(x)+\csc^{2}(x)=(\csc(x)\sec(x))^{2}
verificar cot^2(x)=csc^2(x)	prove\:\cot^{2}(x)=\csc^{2}(x)
verificar 2cot(θ)cot(2θ)=cot^2(-1)	prove\:2\cot(θ)\cot(2θ)=\cot^{2}(-1)
verificar (cos(x))/(sin(x)cot^2(x))=tan(x)	prove\:\frac{\cos(x)}{\sin(x)\cot^{2}(x)}=\tan(x)
verificar (1+sin(α))(1-sin(α))=cos^2(α)	prove\:(1+\sin(α))(1-\sin(α))=\cos^{2}(α)
verificar (tan(x/2))/(1-cos(x))= 1/(sin(x))	prove\:\frac{\tan(\frac{x}{2})}{1-\cos(x)}=\frac{1}{\sin(x)}
verificar ((tan^2(x)))/(sec(x)+1)=((1-cos(x)))/(cos(x))	prove\:\frac{(\tan^{2}(x))}{\sec(x)+1}=\frac{(1-\cos(x))}{\cos(x)}
verificar 1+sin(x)=(csc(x)+1)/(csc(x))	prove\:1+\sin(x)=\frac{\csc(x)+1}{\csc(x)}
verificar 1+sin(θ)=csc(θ)	prove\:1+\sin(θ)=\csc(θ)
verificar (1+sin(x))/(1-sin(x))-(1-sin(x))/(1+sin(x))=(4tan(x))/(cos(x))	prove\:\frac{1+\sin(x)}{1-\sin(x)}-\frac{1-\sin(x)}{1+\sin(x)}=\frac{4\tan(x)}{\cos(x)}
verificar sin(3x)=4sin(x)*cos^2(x)-sin(x)	prove\:\sin(3x)=4\sin(x)\cdot\:\cos^{2}(x)-\sin(x)
verificar sin(θ)= 4/3 sin^3(θ)+1/3 sin^3(θ)	prove\:\sin(θ)=\frac{4}{3}\sin^{3}(θ)+\frac{1}{3}\sin^{3}(θ)
verificar sin(x-(3pi)/2)+sin(pi/2+x)=2cos(x)	prove\:\sin(x-\frac{3π}{2})+\sin(\frac{π}{2}+x)=2\cos(x)
verificar 1/(cos(x)*sin(x))-tan(x)=cot(x)	prove\:\frac{1}{\cos(x)\cdot\:\sin(x)}-\tan(x)=\cot(x)
verificar 1/(csc(x)-1)=sin(x)-1	prove\:\frac{1}{\csc(x)-1}=\sin(x)-1
verificar sec^2(x)cot^2(x)=csc^2(x)	prove\:\sec^{2}(x)\cot^{2}(x)=\csc^{2}(x)
verificar sin(θ)+cot(θ)cos(θ)=csc(θ)	prove\:\sin(θ)+\cot(θ)\cos(θ)=\csc(θ)
verificar cot(θ)+tan(θ)=sec^{(2)}(θ)cot(θ)	prove\:\cot(θ)+\tan(θ)=\sec^{(2)}(θ)\cot(θ)
verificar csc(x)sec(x)=(sec^2(x))/(tan(x))	prove\:\csc(x)\sec(x)=\frac{\sec^{2}(x)}{\tan(x)}
verificar (1+cos(2x))/2 =cos^2(x)	prove\:\frac{1+\cos(2x)}{2}=\cos^{2}(x)
verificar (tan(x))/(1+sec(x))=-cot(x)+csc(x)	prove\:\frac{\tan(x)}{1+\sec(x)}=-\cot(x)+\csc(x)
verificar 1/(1-sin^2(θ))=1+tan^2(θ)	prove\:\frac{1}{1-\sin^{2}(θ)}=1+\tan^{2}(θ)
verificar cos(3x)=4(cos(x))^3-3cos(x)	prove\:\cos(3x)=4(\cos(x))^{3}-3\cos(x)
verificar cos(θ)=sin(pi/2+θ)	prove\:\cos(θ)=\sin(\frac{π}{2}+θ)
verificar 1-8sin^2(θ)cos^2(θ)=cos(4θ)	prove\:1-8\sin^{2}(θ)\cos^{2}(θ)=\cos(4θ)
verificar (cos(b))/(sin(b))*sin(b)=cos(b)	prove\:\frac{\cos(b)}{\sin(b)}\cdot\:\sin(b)=\cos(b)
verificar-50cos(4t)+50=100sin^2(2t)	prove\:-50\cos(4t)+50=100\sin^{2}(2t)
verificar (7sec(θ)-7)/(1-cos(θ))=7sec(θ)	prove\:\frac{7\sec(θ)-7}{1-\cos(θ)}=7\sec(θ)
verificar 1+sec(θ)=(sin(θ)tan(θ))/(1-cos(θ))	prove\:1+\sec(θ)=\frac{\sin(θ)\tan(θ)}{1-\cos(θ)}
verificar cos(20pi+x)+cos(21pi-x)=0	prove\:\cos(20π+x)+\cos(21π-x)=0
verificar ((tan^2(x)+1))/(sec(x))=sec(x)	prove\:\frac{(\tan^{2}(x)+1)}{\sec(x)}=\sec(x)
verificar csc^2(x)cos(2x)=1-tan^2(x)	prove\:\csc^{2}(x)\cos(2x)=1-\tan^{2}(x)
verificar (2tan(θ))/(1-tan^2(θ))=tan(2θ)	prove\:\frac{2\tan(θ)}{1-\tan^{2}(θ)}=\tan(2θ)
verificar cos(x)sin(x)= 1/2 sin(2x)	prove\:\cos(x)\sin(x)=\frac{1}{2}\sin(2x)
verificar (1+tan(x))/(1-tan(x))=tan(x+pi/4)	prove\:\frac{1+\tan(x)}{1-\tan(x)}=\tan(x+\frac{π}{4})
verificar 4sin(x)cos(x)=2sin(2x)	prove\:4\sin(x)\cos(x)=2\sin(2x)
verificar sin^2(a)cos^2(a)+cos^4(a)=cos^2(a)	prove\:\sin^{2}(a)\cos^{2}(a)+\cos^{4}(a)=\cos^{2}(a)
verificar (cot(θ))/(cos(θ))=csc(θ)	prove\:\frac{\cot(θ)}{\cos(θ)}=\csc(θ)
verificar cos^2(2x)= 1/2 (1+cos(4x))	prove\:\cos^{2}(2x)=\frac{1}{2}(1+\cos(4x))
verificar (csc^2(x)-1)/(cot(x))= 1/(tan(x))	prove\:\frac{\csc^{2}(x)-1}{\cot(x)}=\frac{1}{\tan(x)}
verificar sin(4x)=8sin(x)cos(3x)-4sin(x)cos(x)	prove\:\sin(4x)=8\sin(x)\cos(3x)-4\sin(x)\cos(x)
verificar (cot(β))/(csc(β))=cos(β)	prove\:\frac{\cot(β)}{\csc(β)}=\cos(β)
verificar (1+cos(w))/(sin(w))=(sin(w))/(1-cos(w))	prove\:\frac{1+\cos(w)}{\sin(w)}=\frac{\sin(w)}{1-\cos(w)}
verificar (4sec(θ)-4)/(1-cos(θ))=4sec(θ)	prove\:\frac{4\sec(θ)-4}{1-\cos(θ)}=4\sec(θ)
verificar tan^2(θ)=(1-cos^2(θ))/(cos^2(θ))	prove\:\tan^{2}(θ)=\frac{1-\cos^{2}(θ)}{\cos^{2}(θ)}
verificar 1-2cos^2(x)=-1+2sin^2(x)	prove\:1-2\cos^{2}(x)=-1+2\sin^{2}(x)
verificar tan(u)-1tan(u)+1=1-cot(u)1+cot(u)	prove\:\tan(u)-1\tan(u)+1=1-\cot(u)1+\cot(u)
verificar cos(x)=sec(x)-sin(x)tan(x)	prove\:\cos(x)=\sec(x)-\sin(x)\tan(x)
verificar arccsc(x)=sin(x)	prove\:\arccsc(x)=\sin(x)
verificar cot(θ)=(sin(θ))/(cos(θ))	prove\:\cot(θ)=\frac{\sin(θ)}{\cos(θ)}
verificar (1-tan^2(θ))^2=sec^2(θ)-4tan^2(θ)	prove\:(1-\tan^{2}(θ))^{2}=\sec^{2}(θ)-4\tan^{2}(θ)
verificar-cos^2(x)+sin^2(x)=1-2cos^2(x)	prove\:-\cos^{2}(x)+\sin^{2}(x)=1-2\cos^{2}(x)
verificar 4sin(2x)=8sin(x)cos(x)	prove\:4\sin(2x)=8\sin(x)\cos(x)
verificar cos(pi/2-x)csc(x)=1	prove\:\cos(\frac{π}{2}-x)\csc(x)=1

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