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Problemas populares de Trigonometría

verificar (1+csc(a))/(cot(a)+cos(a))=sec(a)	prove\:\frac{1+\csc(a)}{\cot(a)+\cos(a)}=\sec(a)
verificar sec(θ)-sec(θ)sin^2(θ)=cos(θ)	prove\:\sec(θ)-\sec(θ)\sin^{2}(θ)=\cos(θ)
verificar-2=-2cos(0)+15sin(3)(0)	prove\:-2=-2\cos(0)+15\sin(3)(0)
verificar tan(x)-sin(x)=tan(x)sin(x)	prove\:\tan(x)-\sin(x)=\tan(x)\sin(x)
verificar tan(x)cot^2(x)=(cos(x))/(sin(x))	prove\:\tan(x)\cot^{2}(x)=\frac{\cos(x)}{\sin(x)}
verificar sin(x)+(cos(x))/(tan(x))=csc(x)	prove\:\sin(x)+\frac{\cos(x)}{\tan(x)}=\csc(x)
verificar 1/(sin^2(θ))-1/(tan^2(θ))=1	prove\:\frac{1}{\sin^{2}(θ)}-\frac{1}{\tan^{2}(θ)}=1
verificar (5sin(θ)-5sin(θ))^2=25-25sin(2θ)	prove\:(5\sin(θ)-5\sin(θ))^{2}=25-25\sin(2θ)
verificar sin(x)+cos(x)sec^2(x)=sec^2(x)	prove\:\sin(x)+\cos(x)\sec^{2}(x)=\sec^{2}(x)
verificar 1/((sec(y)-tan(y)))=sec(y)+tan(y)	prove\:\frac{1}{(\sec(y)-\tan(y))}=\sec(y)+\tan(y)
verificar tan(θ)(cos(θ)+cot(θ))=sin(θ)+1	prove\:\tan(θ)(\cos(θ)+\cot(θ))=\sin(θ)+1
verificar 2cos(2x)=4cos^2(x)-2	prove\:2\cos(2x)=4\cos^{2}(x)-2
verificar tan(pi/4-θ)=(cos(2θ))/(1+sin(2θ))	prove\:\tan(\frac{π}{4}-θ)=\frac{\cos(2θ)}{1+\sin(2θ)}
verificar (1-sin(2x))/(cos(2x))=(cos(2x))/(1+sin(2x))	prove\:\frac{1-\sin(2x)}{\cos(2x)}=\frac{\cos(2x)}{1+\sin(2x)}
verificar sec(2pi)=sqrt(1-tan^2(2pi))	prove\:\sec(2π)=\sqrt{1-\tan^{2}(2π)}
verificar tan^2(θ)cos^2(θ)=1-cos^2(θ)	prove\:\tan^{2}(θ)\cos^{2}(θ)=1-\cos^{2}(θ)
verificar (sin(x)}{sin(2x)}=\frac{sec(x))/2	prove\:\frac{\sin(x)}{\sin(2x)}=\frac{\sec(x)}{2}
verificar sin(2x)=2sin(x)*cos(x)	prove\:\sin(2x)=2\sin(x)\cdot\:\cos(x)
verificar tan(a) 1/(sin^2(a))=csc(a)sec(a)	prove\:\tan(a)\frac{1}{\sin^{2}(a)}=\csc(a)\sec(a)
verificar (1+csc(x))(1+csc(-x))=-cot^4(x)	prove\:(1+\csc(x))(1+\csc(-x))=-\cot^{4}(x)
verificar 1-(sin^2(t))/(1+cos(t))=cos(t)	prove\:1-\frac{\sin^{2}(t)}{1+\cos(t)}=\cos(t)
verificar (csc(α)+cot(α))(sec(α)-1)=tan(α)	prove\:(\csc(α)+\cot(α))(\sec(α)-1)=\tan(α)
verificar 1-2sin^2(θ)=2cos^2(θ)-1	prove\:1-2\sin^{2}(θ)=2\cos^{2}(θ)-1
verificar sin(pi/4)=cos(pi/4)	prove\:\sin(\frac{π}{4})=\cos(\frac{π}{4})
verificar sec^2(x)cot^2(x)-1=cot^2(x)	prove\:\sec^{2}(x)\cot^{2}(x)-1=\cot^{2}(x)
verificar sin(3a)+sin(a)=4sin(a)-4sin(3a)	prove\:\sin(3a)+\sin(a)=4\sin(a)-4\sin(3a)
verificar tan(β)=(cos(β))/(sin(β)cot^2(β))	prove\:\tan(β)=\frac{\cos(β)}{\sin(β)\cot^{2}(β)}
verificar cos(2θ)=cos^{(2)}(θ)-sin^{(2)}(θ)	prove\:\cos(2θ)=\cos^{(2)}(θ)-\sin^{(2)}(θ)
verificar 2sec(β)=2*1/(cos(β))	prove\:2\sec(β)=2\cdot\:\frac{1}{\cos(β)}
verificar 2cos^2(x)cot(x)=(1+cos(2x))/(tan(x))	prove\:2\cos^{2}(x)\cot(x)=\frac{1+\cos(2x)}{\tan(x)}
verificar (sin^2(x))/(cos(x))=sin(x)tan(x)	prove\:\frac{\sin^{2}(x)}{\cos(x)}=\sin(x)\tan(x)
verificar csc^2(x)sec^2(x)=sec^2(x)+csc^2(x)	prove\:\csc^{2}(x)\sec^{2}(x)=\sec^{2}(x)+\csc^{2}(x)
verificar cot(s)=((sin(2s)))/((1-cos(2s)))	prove\:\cot(s)=\frac{(\sin(2s))}{(1-\cos(2s))}
verificar (3sin^2(x))/(tan^2(x))=3cos^2(x)	prove\:\frac{3\sin^{2}(x)}{\tan^{2}(x)}=3\cos^{2}(x)
verificar (sin(x)+cos(x))/(cos(x))=1+tan(x)	prove\:\frac{\sin(x)+\cos(x)}{\cos(x)}=1+\tan(x)
verificar (1+sin(-x))/(cos(x)tan(x)-1)=-1	prove\:\frac{1+\sin(-x)}{\cos(x)\tan(x)-1}=-1
verificar sec(A)-(cos(A))/(1+sin(A))=tan(A)	prove\:\sec(A)-\frac{\cos(A)}{1+\sin(A)}=\tan(A)
verificar sin(3a)=3sin(a)-sin(a)	prove\:\sin(3a)=3\sin(a)-\sin(a)
verificar (cot(x))/(tan(x))= 1/(tan^2(x))	prove\:\frac{\cot(x)}{\tan(x)}=\frac{1}{\tan^{2}(x)}
verificar 2-sec^2(θ)=1-tan^2(θ)	prove\:2-\sec^{2}(θ)=1-\tan^{2}(θ)
verificar (tan(θ)+sec^2(θ)-sec(θ))/(sec(θ))=tan^2(θ)+sin(θ)	prove\:\frac{\tan(θ)+\sec^{2}(θ)-\sec(θ)}{\sec(θ)}=\tan^{2}(θ)+\sin(θ)
verificar sin((9pi)/4)=sin(3/4 pi+2pi)	prove\:\sin(\frac{9π}{4})=\sin(\frac{3}{4}π+2π)
verificar (cos(2θ))/(sin(2θ))=2cos(2θ)	prove\:\frac{\cos(2θ)}{\sin(2θ)}=2\cos(2θ)
verificar (1-tan^2(A))/(1+tan^2(A))=cos(2A)	prove\:\frac{1-\tan^{2}(A)}{1+\tan^{2}(A)}=\cos(2A)
verificar tan(θ)=(sin(2θ))/(1+cos(2θ))	prove\:\tan(θ)=\frac{\sin(2θ)}{1+\cos(2θ)}
verificar (cot^2(b)-1)/(2cot(b))=cot(2b)	prove\:\frac{\cot^{2}(b)-1}{2\cot(b)}=\cot(2b)
verificar (cos(x)+sin(x))/(sin(x))=1+cot(x)	prove\:\frac{\cos(x)+\sin(x)}{\sin(x)}=1+\cot(x)
verificar sin(pi/3)=cos(pi/6)	prove\:\sin(\frac{π}{3})=\cos(\frac{π}{6})
verificar cos^2(t)=((1+cos(2t)))/2	prove\:\cos^{2}(t)=\frac{(1+\cos(2t))}{2}
verificar cos(-pi/6)=sin((2pi)/3)	prove\:\cos(-\frac{π}{6})=\sin(\frac{2π}{3})
verificar sin(x+pi)-sin(x)+1=0	prove\:\sin(x+π)-\sin(x)+1=0
verificar csc(x)=csc(x)cos^2(x)+sin(x)	prove\:\csc(x)=\csc(x)\cos^{2}(x)+\sin(x)
verificar (sin(x)+cos(x))^2=1+cos(2x)	prove\:(\sin(x)+\cos(x))^{2}=1+\cos(2x)
verificar (sin(x))/(-cos(x))=1	prove\:\frac{\sin(x)}{-\cos(x)}=1
verificar sin(θ)tan(θ)cos(θ)=sin^2(θ)	prove\:\sin(θ)\cdot\:\tan(θ)\cdot\:\cos(θ)=\sin^{2}(θ)
verificar cos^2(x)+sin(x)tan(x)=sec(x)	prove\:\cos^{2}(x)+\sin(x)\tan(x)=\sec(x)
verificar 1/(1-sin(x))=-csc(x)	prove\:\frac{1}{1-\sin(x)}=-\csc(x)
verificar (tan(x))(1+cos(2x))=sin(2x)	prove\:(\tan(x))(1+\cos(2x))=\sin(2x)
verificar cos^2(x)-cos^2(x)=cot^2(x)cos^2(x)	prove\:\cos^{2}(x)-\cos^{2}(x)=\cot^{2}(x)\cos^{2}(x)
verificar 2cos(2(pi/4))=sqrt(16cos(2(pi/4)))	prove\:2\cos(2(\frac{π}{4}))=\sqrt{16\cos(2(\frac{π}{4}))}
verificar-sin(θ)=-sin(-θ)	prove\:-\sin(θ)=-\sin(-θ)
verificar-8cos(2x)-(0)(2cos(2x))=-8cos(2x)	prove\:-8\cos(2x)-(0)(2\cos(2x))=-8\cos(2x)
verificar sec^2(x)cot^2(x)=1+cot^2(x)	prove\:\sec^{2}(x)\cot^{2}(x)=1+\cot^{2}(x)
verificar cos(2B)=(1-tan^2(B))/(1+tan^2(B))	prove\:\cos(2B)=\frac{1-\tan^{2}(B)}{1+\tan^{2}(B)}
verificar sec(u)cos(u)-cos^2(u)=sin^2(u)	prove\:\sec(u)\cos(u)-\cos^{2}(u)=\sin^{2}(u)
verificar (1+sec(x))/(1+cos(x))=sec(x)	prove\:\frac{1+\sec(x)}{1+\cos(x)}=\sec(x)
verificar 2cos^2(x)sec(2x)=sec(2x)+1	prove\:2\cos^{2}(x)\sec(2x)=\sec(2x)+1
verificar (1-sin^2(x))/(sin(x))=cot(x)cos(x)	prove\:\frac{1-\sin^{2}(x)}{\sin(x)}=\cot(x)\cos(x)
verificar tan^2(x)=tan(2x)	prove\:\tan^{2}(x)=\tan(2x)
verificar 7cos^2(x)+5sin^2(x)=cos(2x)+6	prove\:7\cos^{2}(x)+5\sin^{2}(x)=\cos(2x)+6
verificar 1+sec^2(x)=2+tan^2(x)	prove\:1+\sec^{2}(x)=2+\tan^{2}(x)
verificar 9(1+sin(y))(1+sin(-y))=9cos^2(y)	prove\:9(1+\sin(y))(1+\sin(-y))=9\cos^{2}(y)
verificar ((tan(θ))/(sec(θ)))=sin(θ)	prove\:(\frac{\tan(θ)}{\sec(θ)})=\sin(θ)
verificar sin(45)cot(45)=cos(45)	prove\:\sin(45^{\circ\:})\cot(45^{\circ\:})=\cos(45^{\circ\:})
verificar sec(4x)=2	prove\:\sec(4x)=2
verificar 1/(cos^2(A))+1/(cot^2(A))=1	prove\:\frac{1}{\cos^{2}(A)}+\frac{1}{\cot^{2}(A)}=1
verificar csc(θ)-sin(θ)=cot(θ)csc(θ)	prove\:\csc(θ)-\sin(θ)=\cot(θ)\csc(θ)
verificar cos(8θ)=cos^2(4θ)-sin^2(4θ)	prove\:\cos(8θ)=\cos^{2}(4θ)-\sin^{2}(4θ)
verificar 2sec(2α)cos(2α)=2	prove\:2\sec(2α)\cos(2α)=2
verificar 1/(sec(x))+1=(sec(x)+1)/(sec(x))	prove\:\frac{1}{\sec(x)}+1=\frac{\sec(x)+1}{\sec(x)}
verificar tan^2(θ)=sec(θ)csc(θ)tan(θ)-1	prove\:\tan^{2}(θ)=\sec(θ)\csc(θ)\tan(θ)-1
verificar sin(x+y)=cos(pi/2-(x+y))	prove\:\sin(x+y)=\cos(\frac{π}{2}-(x+y))
verificar (sin(x)+cos(x))^2=1+2cos(x)	prove\:(\sin(x)+\cos(x))^{2}=1+2\cos(x)
verificar (csc(x)-1)/(csc^2(x))=cos^2(x)	prove\:\frac{\csc(x)-1}{\csc^{2}(x)}=\cos^{2}(x)
verificar csc(s)-sin(s)=cos(s)cot(s)	prove\:\csc(s)-\sin(s)=\cos(s)\cot(s)
verificar ((4sin^2(x)))/(tan^2(x))=4cos^2(x)	prove\:\frac{(4\sin^{2}(x))}{\tan^{2}(x)}=4\cos^{2}(x)
verificar (tan(2x)+tan(x))/(1-tan(2x)tan(x))=tan(3x)	prove\:\frac{\tan(2x)+\tan(x)}{1-\tan(2x)\tan(x)}=\tan(3x)
verificar csc(x)*(sin(x)+tan(x))=1+sec(x)	prove\:\csc(x)\cdot\:(\sin(x)+\tan(x))=1+\sec(x)
verificar 1-(1-cos^2(x))/(1-cos(x))=-cos(x)	prove\:1-\frac{1-\cos^{2}(x)}{1-\cos(x)}=-\cos(x)
verificar arcsin(2x)= 1/(sin(2x))	prove\:\arcsin(2x)=\frac{1}{\sin(2x)}
verificar cos^2(θ)(1+tan^2(θ))=cos^2(x)	prove\:\cos^{2}(θ)(1+\tan^{2}(θ))=\cos^{2}(x)
verificar (sin(4θ)+sin(2θ))/(cos(4θ)+cos(2θ))=tan(3θ)	prove\:\frac{\sin(4θ)+\sin(2θ)}{\cos(4θ)+\cos(2θ)}=\tan(3θ)
verificar (sin(x)+tan(x))/(sin(x))=1+sec(x)	prove\:\frac{\sin(x)+\tan(x)}{\sin(x)}=1+\sec(x)
verificar (sec(x)+tan(x))^2=((csc(x)+1))/(csc(x)-1)	prove\:(\sec(x)+\tan(x))^{2}=\frac{(\csc(x)+1)}{\csc(x)-1}
verificar (1-cot^2(θ))(sin^2(θ))=1-2cos^2(θ)	prove\:(1-\cot^{2}(θ))(\sin^{2}(θ))=1-2\cos^{2}(θ)
verificar (sin(x))/(-cos(x))=sin(x)+tan(x)	prove\:\frac{\sin(x)}{-\cos(x)}=\sin(x)+\tan(x)
verificar (cot(X)-csc(X))(cot(X)+csc(X))=-1	prove\:(\cot(X)-\csc(X))(\cot(X)+\csc(X))=-1
verificar cos(4x)=cos(3x+x)	prove\:\cos(4x)=\cos(3x+x)
verificar cot(θ)sec(θ)sin(θ)=1	prove\:\cot(θ)\cdot\:\sec(θ)\cdot\:\sin(θ)=1
verificar 1/(sec^2(t))=(1+sin(t))(1-sin(t))	prove\:\frac{1}{\sec^{2}(t)}=(1+\sin(t))(1-\sin(t))

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