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Problemas populares

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Problemas populares de Trigonometría

verificar cos(x+3/2 pi)=sin(x)	prove\:\cos(x+\frac{3}{2}π)=\sin(x)
verificar sin^2(v)+1/(sec^2(v))=1	prove\:\sin^{2}(v)+\frac{1}{\sec^{2}(v)}=1
verificar (csc(θ)sin(θ))/(cot(θ))=tan(θ)	prove\:\frac{\csc(θ)\sin(θ)}{\cot(θ)}=\tan(θ)
verificar 1+tan^2(x)=cos^2(x)+sin^2(x)	prove\:1+\tan^{2}(x)=\cos^{2}(x)+\sin^{2}(x)
verificar (sin(9θ)+sin(3θ))/(cos(9θ)+cos(3θ))=tan(6θ)	prove\:\frac{\sin(9θ)+\sin(3θ)}{\cos(9θ)+\cos(3θ)}=\tan(6θ)
verificar cot^2(A)-cos^2(A)=cot^2(A)cos^2(A)	prove\:\cot^{2}(A)-\cos^{2}(A)=\cot^{2}(A)\cos^{2}(A)
verificar cos^2(2t)+sin^2(2t)=1	prove\:\cos^{2}(2t)+\sin^{2}(2t)=1
verificar tan(α)+cot(2α)=sec(2α)	prove\:\tan(α)+\cot(2α)=\sec(2α)
verificar tan(x+pi/3)=(tan(x)+sqrt(3))/(1-sqrt(3)tan(x))	prove\:\tan(x+\frac{π}{3})=\frac{\tan(x)+\sqrt{3}}{1-\sqrt{3}\tan(x)}
verificar-2sin^2(2θ)=8cos^4(θ)-8cos^2(θ)	prove\:-2\sin^{2}(2θ)=8\cos^{4}(θ)-8\cos^{2}(θ)
verificar csc(x^4)-cot(x^4)=2csc(x)-1	prove\:\csc(x^{4})-\cot(x^{4})=2\csc(x)-1
verificar (csc(θ)-sin(θ))/(cot(θ))=cos(θ)	prove\:\frac{\csc(θ)-\sin(θ)}{\cot(θ)}=\cos(θ)
verificar 1/(sin(x))=arcsin(x)	prove\:\frac{1}{\sin(x)}=\arcsin(x)
verificar (1-2sin^2(x))/(1-sin^2(x))=1-tan(2x)	prove\:\frac{1-2\sin^{2}(x)}{1-\sin^{2}(x)}=1-\tan(2x)
verificar cot(x)=arctan(x)	prove\:\cot(x)=\arctan(x)
verificar 1/(sin(x)cos(x))= 2/(sin(2x))	prove\:\frac{1}{\sin(x)\cos(x)}=\frac{2}{\sin(2x)}
verificar sin(x)tan(x)=1+cos(x)	prove\:\sin(x)\tan(x)=1+\cos(x)
verificar ((1+sin(x))/(cos(x)))^2+((1-sin(x))/(cos(x)))^2=2+4tan^2(x)	prove\:(\frac{1+\sin(x)}{\cos(x)})^{2}+(\frac{1-\sin(x)}{\cos(x)})^{2}=2+4\tan^{2}(x)
verificar sin(x+y)-sin(x-y)=2sin(y)cos(x)	prove\:\sin(x+y)-\sin(x-y)=2\sin(y)\cos(x)
verificar sec^2(x)tan(x)= 1/2 sin(2x)	prove\:\sec^{2}(x)\tan(x)=\frac{1}{2}\sin(2x)
verificar sin(2a)=2cos(a)sin(a)	prove\:\sin(2a)=2\cos(a)\sin(a)
verificar sin(2α)=(2tan(α))/(1+tan^2(α))	prove\:\sin(2α)=\frac{2\tan(α)}{1+\tan^{2}(α)}
verificar (sec(θ)cot(θ))/(csc(θ))=1	prove\:\frac{\sec(θ)\cot(θ)}{\csc(θ)}=1
verificar cos(2x)+2sin^2(x)=1	prove\:\cos(2x)+2\sin^{2}(x)=1
verificar 1/(sin(θ)cos(θ))=sec(θ)csc(θ)	prove\:\frac{1}{\sin(θ)\cos(θ)}=\sec(θ)\csc(θ)
verificar (2tan(x))/(1-tan^2(x))=tan(2x)	prove\:\frac{2\tan(x)}{1-\tan^{2}(x)}=\tan(2x)
verificar sec(x)(tan(x))/(sin(x))=sec^2(x)	prove\:\sec(x)\frac{\tan(x)}{\sin(x)}=\sec^{2}(x)
verificar (1+tan^2(θ))/(csc^2(θ))=tan^2(θ)	prove\:\frac{1+\tan^{2}(θ)}{\csc^{2}(θ)}=\tan^{2}(θ)
verificar (cos(x))/(1-sin(x))=sec(x)tan(x)	prove\:\frac{\cos(x)}{1-\sin(x)}=\sec(x)\tan(x)
verificar sin(3θ)+sin(θ)=2sin(θ)cos(θ)	prove\:\sin(3θ)+\sin(θ)=2\sin(θ)\cos(θ)
verificar (1-cos^2(a))(1+tan^2(a))=tan^2(a)	prove\:(1-\cos^{2}(a))(1+\tan^{2}(a))=\tan^{2}(a)
verificar 1/(sin(13/5))=csc(13/5)	prove\:\frac{1}{\sin(\frac{13}{5})}=\csc(\frac{13}{5})
verificar tan(θ/2)=(1-cos(θ))/2	prove\:\tan(\frac{θ}{2})=\frac{1-\cos(θ)}{2}
verificar-csc(x)+sin(x)=-cos(x)cot(x)	prove\:-\csc(x)+\sin(x)=-\cos(x)\cot(x)
verificar (cos(x)+sin(x))/(sin(x))-cot(x)=1	prove\:\frac{\cos(x)+\sin(x)}{\sin(x)}-\cot(x)=1
verificar cot(x)sec(x)csc^2(x)-cot^3(x)sec(x)=csc(x)	prove\:\cot(x)\sec(x)\csc^{2}(x)-\cot^{3}(x)\sec(x)=\csc(x)
verificar csc(x)+sec(x)= 1/(sin(x)+cos(x))	prove\:\csc(x)+\sec(x)=\frac{1}{\sin(x)+\cos(x)}
verificar (2cot(x))/(sec(x))=2csc(x)-2sin(x)	prove\:\frac{2\cot(x)}{\sec(x)}=2\csc(x)-2\sin(x)
verificar cos(x)*cot(x)+sin(x)=csc(x)	prove\:\cos(x)\cdot\:\cot(x)+\sin(x)=\csc(x)
verificar csc(t)-sin(t)=cot(t)cos(t)	prove\:\csc(t)-\sin(t)=\cot(t)\cos(t)
verificar (sec(x)+1)/(sec(x))=1+cos(x)	prove\:\frac{\sec(x)+1}{\sec(x)}=1+\cos(x)
verificar (cos(A))/(1+sin(A))+tan(A)=sec(A)	prove\:\frac{\cos(A)}{1+\sin(A)}+\tan(A)=\sec(A)
verificar-3cos^2(θ)+11=-5sin(θ)+6	prove\:-3\cos^{2}(θ)+11=-5\sin(θ)+6
verificar (1-tan(x))^2=1-2tan(x)+tan^2(x)	prove\:(1-\tan(x))^{2}=1-2\tan(x)+\tan^{2}(x)
verificar csc(x)cos(x)tan(x)=1	prove\:\csc(x)\cos(x)\tan(x)=1
verificar ((cot^2(x))/(1+cot^2(x)))=cos^2(x)	prove\:(\frac{\cot^{2}(x)}{1+\cot^{2}(x)})=\cos^{2}(x)
verificar (1-cot(-θ))/(cot(-θ))=-tan(θ)-1	prove\:\frac{1-\cot(-θ)}{\cot(-θ)}=-\tan(θ)-1
verificar cos(60)=2cos^2(30)-1	prove\:\cos(60^{\circ\:})=2\cos^{2}(30^{\circ\:})-1
verificar (sin(t)+cos(t))^2=1+sin(2t)	prove\:(\sin(t)+\cos(t))^{2}=1+\sin(2t)
verificar sec^2(θ)= 1/(cos^2(θ))	prove\:\sec^{2}(θ)=\frac{1}{\cos^{2}(θ)}
verificar csc^2(θ)= 1/(sin^2(θ))	prove\:\csc^{2}(θ)=\frac{1}{\sin^{2}(θ)}
verificar sin(x)= 1/2	prove\:\sin(x)=\frac{1}{2}
verificar (2sin(x)cos(x))/(2sin^2(x))=cot(x)	prove\:\frac{2\sin(x)\cos(x)}{2\sin^{2}(x)}=\cot(x)
verificar cos^2(x/2)=(sec(x)+1)/(2sec(x))	prove\:\cos^{2}(\frac{x}{2})=\frac{\sec(x)+1}{2\sec(x)}
verificar (1+cot^2(x))(1-cos(2x))=2	prove\:(1+\cot^{2}(x))(1-\cos(2x))=2
verificar-cot(x/2)=-(csc(x)+cot(x))	prove\:-\cot(\frac{x}{2})=-(\csc(x)+\cot(x))
verificar 1+tan^2(y)=sec^2(y)	prove\:1+\tan^{2}(y)=\sec^{2}(y)
verificar (1+cos(x))/(tan(x)+sin(x))=cot(x)	prove\:\frac{1+\cos(x)}{\tan(x)+\sin(x)}=\cot(x)
verificar 1-(sin(x)+cos(x))^2=-sin(2x)	prove\:1-(\sin(x)+\cos(x))^{2}=-\sin(2x)
verificar (tan^2(x)+1)/(tan^2(x))=csc^2(x)	prove\:\frac{\tan^{2}(x)+1}{\tan^{2}(x)}=\csc^{2}(x)
verificar sin(7x)+sin(x)=2cos(3x)sin(4x)	prove\:\sin(7x)+\sin(x)=2\cos(3x)\sin(4x)
verificar (csc(4x)-cot(4x))/(csc(4x)+cot(4x))=tan(2x)	prove\:\frac{\csc(4x)-\cot(4x)}{\csc(4x)+\cot(4x)}=\tan(2x)
verificar (cos(x/2)-sin(x/2))^2=1-sin(x)	prove\:(\cos(\frac{x}{2})-\sin(\frac{x}{2}))^{2}=1-\sin(x)
verificar 2cos^2(w)-1=1-2sin^2(w)	prove\:2\cos^{2}(w)-1=1-2\sin^{2}(w)
verificar sin(x)(1+cot^2(x))=csc^2(x)	prove\:\sin(x)(1+\cot^{2}(x))=\csc^{2}(x)
verificar (1-cos(x))(1+sec(x))=-sin(x)	prove\:(1-\cos(x))(1+\sec(x))=-\sin(x)
verificar 4cot(x)=cot(x)sin^2(x)	prove\:4\cot(x)=\cot(x)\sin^{2}(x)
verificar 1/(1+tan^2(x))=sin^2(-cos^2(x))	prove\:\frac{1}{1+\tan^{2}(x)}=\sin^{2}(-\cos^{2}(x))
verificar cos^2(7x)-sin^2(7x)=cos(14x)	prove\:\cos^{2}(7x)-\sin^{2}(7x)=\cos(14x)
verificar tan^2(θ)csc^2(θ)=1+tan^2(θ)	prove\:\tan^{2}(θ)\csc^{2}(θ)=1+\tan^{2}(θ)
verificar cos(4a)=8cos^4(a)-8cos^2(a)+1	prove\:\cos(4a)=8\cos^{4}(a)-8\cos^{2}(a)+1
verificar 2cos^2(x)+cos(x)=0	prove\:2\cos^{2}(x)+\cos(x)=0
verificar csc^2(x)sec^2(x)=csc^2(x)+sec^2(x)	prove\:\csc^{2}(x)\sec^{2}(x)=\csc^{2}(x)+\sec^{2}(x)
verificar cos(2θ)=(1-tan^2(θ))/(sec^2(θ))	prove\:\cos(2θ)=\frac{1-\tan^{2}(θ)}{\sec^{2}(θ)}
verificar sin^5(x)=(1-2cos^2(x)+cos^4(x))(sin(x))	prove\:\sin^{5}(x)=(1-2\cos^{2}(x)+\cos^{4}(x))(\sin(x))
verificar (sin(x)+cos(x))^2=1+2cos(x)sin(x)	prove\:(\sin(x)+\cos(x))^{2}=1+2\cos(x)\sin(x)
verificar 2cos^2(x)=1	prove\:2\cos^{2}(x)=1
verificar (cos(a))/(sin(a)cot(a))=1	prove\:\frac{\cos(a)}{\sin(a)\cot(a)}=1
verificar 2(cos(3θ)+3cos(θ))=8cos^3(θ)	prove\:2(\cos(3θ)+3\cos(θ))=8\cos^{3}(θ)
verificar sin^2(t/2)=(1-cos(t))/2	prove\:\sin^{2}(\frac{t}{2})=\frac{1-\cos(t)}{2}
verificar cos(θ)=(sec(θ)+tan(θ))(1-sin(θ))	prove\:\cos(θ)=(\sec(θ)+\tan(θ))(1-\sin(θ))
verificar (cos(x))/(sin(2x))= 1/(2sin(x))	prove\:\frac{\cos(x)}{\sin(2x)}=\frac{1}{2\sin(x)}
verificar sec(2x)= 1/(cos(2x))	prove\:\sec(2x)=\frac{1}{\cos(2x)}
verificar (sin(6x)+sin(2x))/(cos(6x)-cos(2x))=-cot(2x)	prove\:\frac{\sin(6x)+\sin(2x)}{\cos(6x)-\cos(2x)}=-\cot(2x)
verificar (sin(x)+cos(x))2=1+sin(2x)	prove\:(\sin(x)+\cos(x))2=1+\sin(2x)
verificar cot(x)cos(x)=csc(x)-sin(x)	prove\:\cot(x)\cos(x)=\csc(x)-\sin(x)
verificar sec(2α)2-sec(2α)=sec(2α)	prove\:\sec(2α)2-\sec(2α)=\sec(2α)
verificar (sin(2θ))/(sin(4θ))= 1/2 sec(2θ)	prove\:\frac{\sin(2θ)}{\sin(4θ)}=\frac{1}{2}\sec(2θ)
verificar (sin(2x))/(cos(x))=2sin(x)	prove\:\frac{\sin(2x)}{\cos(x)}=2\sin(x)
verificar 1-cos^2(2x)=sin^2(2x)	prove\:1-\cos^{2}(2x)=\sin^{2}(2x)
verificar (cos^2(x)-1)/(cos(x)-1)=cos(x)+1	prove\:\frac{\cos^{2}(x)-1}{\cos(x)-1}=\cos(x)+1
verificar cosh^{(2)}(x)-sinh^{(2)}(x)=1	prove\:\cosh^{(2)}(x)-\sinh^{(2)}(x)=1
verificar sin(2x)-cos(2x)=1-2cos(2x)	prove\:\sin(2x)-\cos(2x)=1-2\cos(2x)
verificar cot^2(x)tan(x)sin(x)=cos(x)	prove\:\cot^{2}(x)\tan(x)\sin(x)=\cos(x)
verificar tan(x)(csc^{(2)}(x)-1)=cot(x)	prove\:\tan(x)(\csc^{(2)}(x)-1)=\cot(x)
verificar sin^4(θ)-cos^4(θ)=2sin(θ)-1	prove\:\sin^{4}(θ)-\cos^{4}(θ)=2\sin(θ)-1
verificar tan(x)-sqrt(3)=0	prove\:\tan(x)-\sqrt{3}=0
verificar (sin^4(x)-1)/(cos^2(x))=cos^2(x)-2	prove\:\frac{\sin^{4}(x)-1}{\cos^{2}(x)}=\cos^{2}(x)-2
verificar csc(x)tan(x)= 1/(cos(x))	prove\:\csc(x)\tan(x)=\frac{1}{\cos(x)}
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)

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