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Problemas populares de Trigonometría

verificar cot(-x)cos(-x)+sin(-x)=-csc(x)	prove\:\cot(-x)\cos(-x)+\sin(-x)=-\csc(x)
verificar cot(θ)+tan(θ)=csc(θ)sec(θ)	prove\:\cot(θ)+\tan(θ)=\csc(θ)\sec(θ)
verificar 1/(1-sin^2(x))=1+tan^2(x)	prove\:\frac{1}{1-\sin^{2}(x)}=1+\tan^{2}(x)
verificar tan(pi/4+a)-tan(pi/4-a)=2tan(2a)	prove\:\tan(\frac{π}{4}+a)-\tan(\frac{π}{4}-a)=2\tan(2a)
verificar sin^2(x)+3cos^2(x)=3-2sin^2(x)	prove\:\sin^{2}(x)+3\cos^{2}(x)=3-2\sin^{2}(x)
verificar 0=cot(x)sin(x)-cos^2(x)sec(x)	prove\:0=\cot(x)\sin(x)-\cos^{2}(x)\sec(x)
verificar (1-tan^2(x))/(sec^2(x))=cos(2x)	prove\:\frac{1-\tan^{2}(x)}{\sec^{2}(x)}=\cos(2x)
verificar tan^2(x)+1= 1/(cos^2(x))	prove\:\tan^{2}(x)+1=\frac{1}{\cos^{2}(x)}
verificar (1+tan^2(θ))/(sec(θ))=sec(θ)	prove\:\frac{1+\tan^{2}(θ)}{\sec(θ)}=\sec(θ)
verificar cot(θ)+(sin(θ))/(1+cos(θ))=csc(θ)	prove\:\cot(θ)+\frac{\sin(θ)}{1+\cos(θ)}=\csc(θ)
verificar (sin(pi/2+x))/(sin(pi-x))=cot(x)	prove\:\frac{\sin(\frac{π}{2}+x)}{\sin(π-x)}=\cot(x)
verificar cos(x)*csc(x)=cot(x)	prove\:\cos(x)\cdot\:\csc(x)=\cot(x)
verificar sin(4x)=4sin(x)cos(x)cos(2x)	prove\:\sin(4x)=4\sin(x)\cos(x)\cos(2x)
verificar (cot(-θ))/(csc(θ))=-cos(θ)	prove\:\frac{\cot(-θ)}{\csc(θ)}=-\cos(θ)
verificar sec(α)-cos(α)=sin(α)tan(α)	prove\:\sec(α)-\cos(α)=\sin(α)\tan(α)
verificar csc(x)=(1+sec(x))/(sin(x)+tan(x))	prove\:\csc(x)=\frac{1+\sec(x)}{\sin(x)+\tan(x)}
verificar tan^2(θ)+6=sec^2(θ)+5	prove\:\tan^{2}(θ)+6=\sec^{2}(θ)+5
verificar (cos(x))/(1+sin(x))+tan(x)=sec(x)	prove\:\frac{\cos(x)}{1+\sin(x)}+\tan(x)=\sec(x)
verificar sec(pi/2-x)=csc(x)	prove\:\sec(\frac{π}{2}-x)=\csc(x)
verificar 1/(csc(x)-1)+1/(csc(x)+1)=2tan(x)sec(x)	prove\:\frac{1}{\csc(x)-1}+\frac{1}{\csc(x)+1}=2\tan(x)\sec(x)
verificar (1+cos(t))/(1-cos(t))=(csc(t)+cot(t))^2	prove\:\frac{1+\cos(t)}{1-\cos(t)}=(\csc(t)+\cot(t))^{2}
verificar sec^2(α)+csc^2(α)= 1/(sin^2(α)cos^2(α))	prove\:\sec^{2}(α)+\csc^{2}(α)=\frac{1}{\sin^{2}(α)\cos^{2}(α)}
verificar sin^2(A)+cos^2(A)=1	prove\:\sin^{2}(A)+\cos^{2}(A)=1
verificar tan(x)=sin(x)sec(x)	prove\:\tan(x)=\sin(x)\sec(x)
verificar (1+cot^2(θ))(1-cos^2(θ))=1	prove\:(1+\cot^{2}(θ))(1-\cos^{2}(θ))=1
verificar csc(2x)+cot(2x)=cot(x)	prove\:\csc(2x)+\cot(2x)=\cot(x)
verificar cos^2(t)=(1+cos(2t))/2	prove\:\cos^{2}(t)=\frac{1+\cos(2t)}{2}
verificar cos(x)csc(x)tan(x)=1	prove\:\cos(x)\csc(x)\tan(x)=1
verificar cos(x)(csc(x)+sec(x))=cot(x)+1	prove\:\cos(x)(\csc(x)+\sec(x))=\cot(x)+1
verificar sec(θ)cot(θ)=csc(θ)	prove\:\sec(θ)\cot(θ)=\csc(θ)
verificar cos(x-pi)=-cos(x)	prove\:\cos(x-π)=-\cos(x)
verificar (csc^2(θ))/(1+tan^2(θ))=cot^2(θ)	prove\:\frac{\csc^{2}(θ)}{1+\tan^{2}(θ)}=\cot^{2}(θ)
verificar (tan(y))/(csc(y))=sec(y)-cos(y)	prove\:\frac{\tan(y)}{\csc(y)}=\sec(y)-\cos(y)
verificar cos(3x)=cos(2x+x)	prove\:\cos(3x)=\cos(2x+x)
verificar sin^2(x)-1=-cos^2(x)	prove\:\sin^{2}(x)-1=-\cos^{2}(x)
verificar 2-csc^2(x)=1-cot^2(x)	prove\:2-\csc^{2}(x)=1-\cot^{2}(x)
verificar 1-sin^2(θ)=cos^2(θ)	prove\:1-\sin^{2}(θ)=\cos^{2}(θ)
verificar sin(8x)=2sin(4x)cos(4x)	prove\:\sin(8x)=2\sin(4x)\cos(4x)
verificar sin(t)csc(pi/2-t)=tan(t)	prove\:\sin(t)\csc(\frac{π}{2}-t)=\tan(t)
verificar cos(x)cot(x)=csc(x)-sin(x)	prove\:\cos(x)\cot(x)=\csc(x)-\sin(x)
verificar (tan(x))/(csc(x))=sec(x)-cos(x)	prove\:\frac{\tan(x)}{\csc(x)}=\sec(x)-\cos(x)
verificar sec(x)-tan(x)= 1/(sec(x)+tan(x))	prove\:\sec(x)-\tan(x)=\frac{1}{\sec(x)+\tan(x)}
verificar (1+tan^2(x))/(1+cot^2(x))=tan^2(x)	prove\:\frac{1+\tan^{2}(x)}{1+\cot^{2}(x)}=\tan^{2}(x)
verificar 1/(tan(β))+tan(β)=sec(β)csc(β)	prove\:\frac{1}{\tan(β)}+\tan(β)=\sec(β)\csc(β)
verificar (cos(2x))/(sin(x))=cos(x)cot(x)-sin(x)	prove\:\frac{\cos(2x)}{\sin(x)}=\cos(x)\cot(x)-\sin(x)
verificar cot^2(2x)+cos^2(2x)+sin^2(2x)=csc^2(2x)	prove\:\cot^{2}(2x)+\cos^{2}(2x)+\sin^{2}(2x)=\csc^{2}(2x)
verificar sin^2(x)-4cos^2(x)=1-5cos^2(x)	prove\:\sin^{2}(x)-4\cos^{2}(x)=1-5\cos^{2}(x)
verificar 25sec^2(5x)=25+(5tan(5x))^2	prove\:25\sec^{2}(5x)=25+(5\tan(5x))^{2}
verificar tan(x)=csc(2x)-cot(2x)	prove\:\tan(x)=\csc(2x)-\cot(2x)
verificar sin^2(-x)+cos^2(-x)=1	prove\:\sin^{2}(-x)+\cos^{2}(-x)=1
verificar (sec(x)-cos(x))/(tan(x))=sin(x)	prove\:\frac{\sec(x)-\cos(x)}{\tan(x)}=\sin(x)
verificar sin(2x)=2cos(x)sin(x)	prove\:\sin(2x)=2\cos(x)\sin(x)
verificar cos(x+pi)=-cos(x)	prove\:\cos(x+π)=-\cos(x)
verificar sin(x)sec(x)cot(x)=1	prove\:\sin(x)\sec(x)\cot(x)=1
verificar tan(2u)=(2cot(u))/(csc^2(u)-2)	prove\:\tan(2u)=\frac{2\cot(u)}{\csc^{2}(u)-2}
verificar (sin(x))^2+(cos(x))^2=1	prove\:(\sin(x))^{2}+(\cos(x))^{2}=1
verificar csc^2(x)cos^2(x)=csc^2(x)-1	prove\:\csc^{2}(x)\cos^{2}(x)=\csc^{2}(x)-1
verificar 1-2cos^2(x)+cos^4(x)=sin^4(x)	prove\:1-2\cos^{2}(x)+\cos^{4}(x)=\sin^{4}(x)
verificar sec(x)-(cos(x))/(1+sin(x))=tan(x)	prove\:\sec(x)-\frac{\cos(x)}{1+\sin(x)}=\tan(x)
verificar tan(x)+cot(x)=(sec(x))(csc(x))	prove\:\tan(x)+\cot(x)=(\sec(x))(\csc(x))
verificar sin(x)+sin(x)tan^2(x)=tan(x)sec(x)	prove\:\sin(x)+\sin(x)\tan^{2}(x)=\tan(x)\sec(x)
verificar sin(θ)(csc(θ)-sin(θ))=cos^2(θ)	prove\:\sin(θ)(\csc(θ)-\sin(θ))=\cos^{2}(θ)
verificar sec(y)cos(y)=1	prove\:\sec(y)\cos(y)=1
verificar csc(x)-sin(x)=cos(x)*cot(x)	prove\:\csc(x)-\sin(x)=\cos(x)\cdot\:\cot(x)
verificar 1=sin^2(x)+cos^2(x)	prove\:1=\sin^{2}(x)+\cos^{2}(x)
verificar (sec^2(θ))/(tan(θ))=sec(θ)csc(θ)	prove\:\frac{\sec^{2}(θ)}{\tan(θ)}=\sec(θ)\csc(θ)
verificar sec(2x)=(1+tan^2(x))/(1-tan^2(x))	prove\:\sec(2x)=\frac{1+\tan^{2}(x)}{1-\tan^{2}(x)}
verificar cos(x)+tan(x)sin(x)=sec(x)	prove\:\cos(x)+\tan(x)\sin(x)=\sec(x)
verificar cos^2(x)-sin^2(x)=cos(2x)	prove\:\cos^{2}(x)-\sin^{2}(x)=\cos(2x)
verificar sec^2(θ)(1-cos^2(θ))=tan^2(θ)	prove\:\sec^{2}(θ)(1-\cos^{2}(θ))=\tan^{2}(θ)
verificar cos^2(θ)+tan^2(θ)cos^2(θ)=1	prove\:\cos^{2}(θ)+\tan^{2}(θ)\cos^{2}(θ)=1
verificar 1-cos(x)=sin(x)	prove\:1-\cos(x)=\sin(x)
verificar csc(x)-sin(x)=cot(x)*cos(x)	prove\:\csc(x)-\sin(x)=\cot(x)\cdot\:\cos(x)
verificar sin^4(y)-cos^4(y)=1-2cos^2(y)	prove\:\sin^{4}(y)-\cos^{4}(y)=1-2\cos^{2}(y)
verificar 1-sin^2(-θ)=cos^2(θ)	prove\:1-\sin^{2}(-θ)=\cos^{2}(θ)
verificar tan(θ)csc^2(θ)-tan(θ)=cot(θ)	prove\:\tan(θ)\csc^{2}(θ)-\tan(θ)=\cot(θ)
verificar (1+sec(θ))/(csc(θ))-tan(θ)=sin(θ)	prove\:\frac{1+\sec(θ)}{\csc(θ)}-\tan(θ)=\sin(θ)
verificar (1+cot(x))/(1+tan(x))=cot(x)	prove\:\frac{1+\cot(x)}{1+\tan(x)}=\cot(x)
verificar cos(α+β)+cos(α-β)=2cos(α)cos(β)	prove\:\cos(α+β)+\cos(α-β)=2\cos(α)\cos(β)
verificar (1-cos^2(x))/(cos^2(x))=tan^2(x)	prove\:\frac{1-\cos^{2}(x)}{\cos^{2}(x)}=\tan^{2}(x)
verificar (1-cos(2x))/(1+cos(2x))=tan^2(x)	prove\:\frac{1-\cos(2x)}{1+\cos(2x)}=\tan^{2}(x)
verificar tan^2(θ/2)=(sec(θ)-1)/(sec(θ)+1)	prove\:\tan^{2}(\frac{θ}{2})=\frac{\sec(θ)-1}{\sec(θ)+1}
verificar (sec(x))/(tan(x))=csc(x)	prove\:\frac{\sec(x)}{\tan(x)}=\csc(x)
verificar (1-sin(v))/(cos(v))+(cos(v))/(1-sin(v))=2sec(v)	prove\:\frac{1-\sin(v)}{\cos(v)}+\frac{\cos(v)}{1-\sin(v)}=2\sec(v)
verificar sec(θ)-tan(θ)= 1/(sec(θ)+tan(θ))	prove\:\sec(θ)-\tan(θ)=\frac{1}{\sec(θ)+\tan(θ)}
verificar sec(x)=(1+csc(x))/(cot(x)+cos(x))	prove\:\sec(x)=\frac{1+\csc(x)}{\cot(x)+\cos(x)}
verificar 9sec^2(θ)-5tan^2(θ)=5+4sec^2(θ)	prove\:9\sec^{2}(θ)-5\tan^{2}(θ)=5+4\sec^{2}(θ)
verificar cot(2θ)=cot(θ)-1/2 sec(θ)csc(θ)	prove\:\cot(2θ)=\cot(θ)-\frac{1}{2}\sec(θ)\csc(θ)
verificar (csc(x)-cot(x))(csc(x)+cot(x))=1	prove\:(\csc(x)-\cot(x))(\csc(x)+\cot(x))=1
verificar (tan(x))(sin(x))=sec(x)-cos(x)	prove\:(\tan(x))(\sin(x))=\sec(x)-\cos(x)
verificar tan(α)+cot(α)=sec(α)csc(α)	prove\:\tan(α)+\cot(α)=\sec(α)\csc(α)
verificar (cos(x)-sin(x))^2=1-sin(2x)	prove\:(\cos(x)-\sin(x))^{2}=1-\sin(2x)
verificar (cos(x+y))/(cos(x-y))=(cot(y)-tan(x))/(cot(y)+tan(x))	prove\:\frac{\cos(x+y)}{\cos(x-y)}=\frac{\cot(y)-\tan(x)}{\cot(y)+\tan(x)}
verificar cot(x)tan(x)=1	prove\:\cot(x)\tan(x)=1
verificar cos^2(a)-sin^2(a)=1-2sin^2(a)	prove\:\cos^{2}(a)-\sin^{2}(a)=1-2\sin^{2}(a)
verificar tan(u)cot(u)-sin^2(u)=cos^2(u)	prove\:\tan(u)\cot(u)-\sin^{2}(u)=\cos^{2}(u)
verificar 1-2sin^2(2x)=8cos^4(x)-8cos^2(x)+1	prove\:1-2\sin^{2}(2x)=8\cos^{4}(x)-8\cos^{2}(x)+1
verificar sin(pi/4)=(sqrt(2))/2	prove\:\sin(\frac{π}{4})=\frac{\sqrt{2}}{2}
verificar (sin(x))/(cot(x)+csc(x))=1-cos(x)	prove\:\frac{\sin(x)}{\cot(x)+\csc(x)}=1-\cos(x)
verificar tan(a)cos(a)=sin(a)	prove\:\tan(a)\cos(a)=\sin(a)

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