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Problemas populares

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Problemas populares de Trigonometría

verificar cos(2x)=cos(-2x)	prove\:\cos(2x)=\cos(-2x)
verificar tan(x)*csc(x)=sec(x)	prove\:\tan(x)\cdot\:\csc(x)=\sec(x)
verificar tan(θ)sin(θ)=2sin^2(θ)	prove\:\tan(θ)\sin(θ)=2\sin^{2}(θ)
verificar-2cos^2(θ)=sin^4(θ)-cos^4(θ)-1	prove\:-2\cos^{2}(θ)=\sin^{4}(θ)-\cos^{4}(θ)-1
verificar sqrt(3)csc(x)cot(x)+3csc(x)=0	prove\:\sqrt{3}\csc(x)\cot(x)+3\csc(x)=0
verificar sin^2(pi/2)=1-cos^2(pi/2)	prove\:\sin^{2}(\frac{π}{2})=1-\cos^{2}(\frac{π}{2})
verificar cot(θ)-tan(θ)=(2cos(2θ))/(sin(2θ))	prove\:\cot(θ)-\tan(θ)=\frac{2\cos(2θ)}{\sin(2θ)}
verificar (sec^2(x))/(tan(x))=2csc(2x)	prove\:\frac{\sec^{2}(x)}{\tan(x)}=2\csc(2x)
verificar tan(-u)*sin(-u)+cos(-u)=sec(u)	prove\:\tan(-u)\cdot\:\sin(-u)+\cos(-u)=\sec(u)
verificar (2sin^2(x))/(sin(2x))= 1/(cot(x))	prove\:\frac{2\sin^{2}(x)}{\sin(2x)}=\frac{1}{\cot(x)}
verificar csc(x)(csc(x)+sin(-x))=cot^2(x)	prove\:\csc(x)(\csc(x)+\sin(-x))=\cot^{2}(x)
verificar 2/(1+sin(θ))=(sec(θ)-tan(θ))^2+1	prove\:\frac{2}{1+\sin(θ)}=(\sec(θ)-\tan(θ))^{2}+1
verificar tan(x)+cot(x)=(sec(x))*(csc(x))	prove\:\tan(x)+\cot(x)=(\sec(x))\cdot\:(\csc(x))
verificar (csc(θ)sin(θ))/(cos(θ))=sec(θ)	prove\:\frac{\csc(θ)\sin(θ)}{\cos(θ)}=\sec(θ)
verificar cos(-pi/4)= 1/(sqrt(2))	prove\:\cos(-\frac{π}{4})=\frac{1}{\sqrt{2}}
verificar (tan(x)+cot(x))/(sec(x)csc(x))=1	prove\:\frac{\tan(x)+\cot(x)}{\sec(x)\csc(x)}=1
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)
verificar tan(θ)sin(20)=2sin^2(θ)	prove\:\tan(θ)\sin(20^{\circ\:})=2\sin^{2}(θ)
verificar 1/(1-sin(x))=-1/(sin(x))	prove\:\frac{1}{1-\sin(x)}=-\frac{1}{\sin(x)}
verificar tan(-a)=-tan(a)	prove\:\tan(-a)=-\tan(a)
verificar (tan(y)+cos(y))/(1+sin(y))=sec(y)	prove\:\frac{\tan(y)+\cos(y)}{1+\sin(y)}=\sec(y)
verificar sin^2(x)+cos(2x)=1-sin^2(x)	prove\:\sin^{2}(x)+\cos(2x)=1-\sin^{2}(x)
verificar cos(45)=(sin(245))/(2sin(45))	prove\:\cos(45^{\circ\:})=\frac{\sin(2\cdot\:45^{\circ\:})}{2\cdot\:\sin(45^{\circ\:})}
verificar 4sin(3x)cos(4x)=2sin(7x)-2sin(x)	prove\:4\sin(3x)\cos(4x)=2\sin(7x)-2\sin(x)
verificar sec^2(x)=(sec(x))/(cos(x))	prove\:\sec^{2}(x)=\frac{\sec(x)}{\cos(x)}
verificar cot(θ)*sin(θ)=cos(θ)	prove\:\cot(θ)\cdot\:\sin(θ)=\cos(θ)
verificar 2sin^2(θ)+sin(θ)-1=0	prove\:2\sin^{2}(θ)+\sin(θ)-1=0
verificar 1/(csc(t)-cot(t))=csc(t)+cot(t)	prove\:\frac{1}{\csc(t)-\cot(t)}=\csc(t)+\cot(t)
verificar sin((5pi)/2+x)=cos(x)	prove\:\sin(\frac{5π}{2}+x)=\cos(x)
verificar 2/(cos^2(x)-tan^2(x))=2+tan^2(x)	prove\:\frac{2}{\cos^{2}(x)-\tan^{2}(x)}=2+\tan^{2}(x)
verificar cos(x)=sin(x+pi/6)-sin(x-pi/6)	prove\:\cos(x)=\sin(x+\frac{π}{6})-\sin(x-\frac{π}{6})
verificar tan^2(pi/4)=tan(pi/4)	prove\:\tan^{2}(\frac{π}{4})=\tan(\frac{π}{4})
verificar 1-sin(x)cos(x)cot(x)=sin^2(x)	prove\:1-\sin(x)\cos(x)\cot(x)=\sin^{2}(x)
verificar sec(A)-tan(A)=(cos(A))/(1+sin(A))	prove\:\sec(A)-\tan(A)=\frac{\cos(A)}{1+\sin(A)}
verificar (cos(θ)+sin(θ))^2=1+2cos(θ)sin(θ)	prove\:(\cos(θ)+\sin(θ))^{2}=1+2\cos(θ)\sin(θ)
verificar sin^2(θ)= 3/4 sin(θ)-1/4 sin(3θ)	prove\:\sin^{2}(θ)=\frac{3}{4}\sin(θ)-\frac{1}{4}\sin(3θ)
verificar (1+tan^2(x))/(cos^2(x))=sec^4(x)	prove\:\frac{1+\tan^{2}(x)}{\cos^{2}(x)}=\sec^{4}(x)
verificar (tan^2(x))/(sec(x)+1)=sec(x)	prove\:\frac{\tan^{2}(x)}{\sec(x)+1}=\sec(x)
verificar sin^3(x)+cos^3(x)tan(x)=sin(x)	prove\:\sin^{3}(x)+\cos^{3}(x)\tan(x)=\sin(x)
verificar (sin(x)-cos(x))^2+sin(2x)=1	prove\:(\sin(x)-\cos(x))^{2}+\sin(2x)=1
verificar tan^3(x)=(tan(x))^3	prove\:\tan^{3}(x)=(\tan(x))^{3}
verificar (csc(x)+tan(x))cos(x)=sin(x)cot(x)	prove\:(\csc(x)+\tan(x))\cos(x)=\sin(x)\cot(x)
verificar 3tan^2(x)+13tan(x)=4	prove\:3\tan^{2}(x)+13\tan(x)=4
verificar csc(pi/2-θ)=sec(θ)	prove\:\csc(\frac{π}{2}-θ)=\sec(θ)
verificar sin(x)cos(x)=cot(x)	prove\:\sin(x)\cos(x)=\cot(x)
verificar (sin(a+2a)+4sin^3(a))/3 =sin(a)	prove\:\frac{\sin(a+2a)+4\sin^{3}(a)}{3}=\sin(a)
verificar-sin^2(x)=-((1-cos(2x)))/2	prove\:-\sin^{2}(x)=-\frac{(1-\cos(2x))}{2}
verificar cos(1*pi)=-1	prove\:\cos(1\cdot\:π)=-1
verificar (sin^2(x))/(sin(x)cos(x))=tan(x)	prove\:\frac{\sin^{2}(x)}{\sin(x)\cos(x)}=\tan(x)
verificar cos(60+θ)-cos(60-θ)=-sqrt(3)sin(θ)	prove\:\cos(60^{\circ\:}+θ)-\cos(60^{\circ\:}-θ)=-\sqrt{3}\sin(θ)
verificar cos(θ)cot(θ)= 1/(sin(θ))-sin(θ)	prove\:\cos(θ)\cot(θ)=\frac{1}{\sin(θ)}-\sin(θ)
verificar-sin(x)=1-(cos^2(x))/(1-sin(x))	prove\:-\sin(x)=1-\frac{\cos^{2}(x)}{1-\sin(x)}
verificar sin^4(a)-cos^4(a)=2sin^2(a)-1	prove\:\sin^{4}(a)-\cos^{4}(a)=2\sin^{2}(a)-1
verificar 1+(cos^2(x))/(sin^2(x))=csc^2(x)	prove\:1+\frac{\cos^{2}(x)}{\sin^{2}(x)}=\csc^{2}(x)
verificar 1-cos(θ)sin(θ)tan(θ)=cos^2(θ)	prove\:1-\cos(θ)\sin(θ)\tan(θ)=\cos^{2}(θ)
verificar (2sin(x)+2cos(x))^2=4sin(2x)+4	prove\:(2\sin(x)+2\cos(x))^{2}=4\sin(2x)+4
verificar (1-sin^2(A))/(1-cos^2(A))=cot^2(A)	prove\:\frac{1-\sin^{2}(A)}{1-\cos^{2}(A)}=\cot^{2}(A)
verificar (sin(60))/(cos(60))=tan(60)	prove\:\frac{\sin(60^{\circ\:})}{\cos(60^{\circ\:})}=\tan(60^{\circ\:})
verificar cos(x)csc(x)=cos(x)	prove\:\cos(x)\csc(x)=\cos(x)
verificar cot(x)+1/(cot(x))= 2/(sin(2x))	prove\:\cot(x)+\frac{1}{\cot(x)}=\frac{2}{\sin(2x)}
verificar sec^2(t)=cos^{-2}(t)	prove\:\sec^{2}(t)=\cos^{-2}(t)
verificar (tan(x)*cot(x))/(csc(x))=sin(x)	prove\:\frac{\tan(x)\cdot\:\cot(x)}{\csc(x)}=\sin(x)
verificar 1/(sin^2(x)tan(x))=csc^2(x)cot(x)	prove\:\frac{1}{\sin^{2}(x)\tan(x)}=\csc^{2}(x)\cot(x)
verificar sec(x)-cos(x)=(sin(x))(tan(x))	prove\:\sec(x)-\cos(x)=(\sin(x))(\tan(x))
verificar 1/(cos^2(x))-1/(cot^2(x))=1	prove\:\frac{1}{\cos^{2}(x)}-\frac{1}{\cot^{2}(x)}=1
verificar 1/(1+cot^2(a))=sin^2(a)	prove\:\frac{1}{1+\cot^{2}(a)}=\sin^{2}(a)
verificar tan(x/2)(1+cos(x))=sin(x)	prove\:\tan(\frac{x}{2})(1+\cos(x))=\sin(x)
verificar 1-((cos^2(x))/((1+sin(x))))=sin(x)	prove\:1-(\frac{\cos^{2}(x)}{(1+\sin(x))})=\sin(x)
verificar (tan(θ))/(cot(θ))+1=sec^2(θ)	prove\:\frac{\tan(θ)}{\cot(θ)}+1=\sec^{2}(θ)
verificar (sin(6x)+sin(10x))/(cos(6x)+cos(10x))=tan(8x)	prove\:\frac{\sin(6x)+\sin(10x)}{\cos(6x)+\cos(10x)}=\tan(8x)
verificar sin(0)=(0)^3	prove\:\sin(0)=(0)^{3}
verificar tan(2x)=-(arctan(-4/3))/2	prove\:\tan(2x)=-\frac{\arctan(-\frac{4}{3})}{2}
verificar cos(0+pi/2)=-sin(0)	prove\:\cos(0+\frac{π}{2})=-\sin(0)
verificar sin^{(2)}(a/2)=(1-cos(a))/2	prove\:\sin^{(2)}(\frac{a}{2})=\frac{1-\cos(a)}{2}
verificar (1+sec(x))/(tan(x))=cot(x)+csc(x)	prove\:\frac{1+\sec(x)}{\tan(x)}=\cot(x)+\csc(x)
verificar cot^2(x)=(1+cos(2x))/(1-cos(2x))	prove\:\cot^{2}(x)=\frac{1+\cos(2x)}{1-\cos(2x)}
verificar cos(pi+x)=cos(x)	prove\:\cos(π+x)=\cos(x)
verificar sec(2x)=((sec^2(x)))/(1-tan^2(x))	prove\:\sec(2x)=\frac{(\sec^{2}(x))}{1-\tan^{2}(x)}
verificar (sin^2(x)-1)^2=cos(2x)+sin^4(x)	prove\:(\sin^{2}(x)-1)^{2}=\cos(2x)+\sin^{4}(x)
verificar sec(x)-cos(x)=sin^2(x)sec(x)	prove\:\sec(x)-\cos(x)=\sin^{2}(x)\sec(x)
verificar csc^4(x)-cot^4(x)=2csc^2(x)+1	prove\:\csc^{4}(x)-\cot^{4}(x)=2\csc^{2}(x)+1
verificar (1-cos(x))(1+sec(x))=sin(x)cos(x)	prove\:(1-\cos(x))(1+\sec(x))=\sin(x)\cos(x)
verificar 2sin^2(x)=1	prove\:2\sin^{2}(x)=1
verificar (1-cos^2(θ))/(1-sin^2(θ))=tan^2(θ)	prove\:\frac{1-\cos^{2}(θ)}{1-\sin^{2}(θ)}=\tan^{2}(θ)
verificar sin^2(t)= 1/2-1/2 cos(2t)	prove\:\sin^{2}(t)=\frac{1}{2}-\frac{1}{2}\cos(2t)
verificar cos(3x)=4(cos^3(x))-3cos(x)	prove\:\cos(3x)=4(\cos^{3}(x))-3\cos(x)
verificar (1+csc(x))/(sec(x))=cot(x)cos(x)	prove\:\frac{1+\csc(x)}{\sec(x)}=\cot(x)\cos(x)
verificar cos^2(x)-sin^2(x)=1+2sin^2(x)	prove\:\cos^{2}(x)-\sin^{2}(x)=1+2\sin^{2}(x)
verificar cot(θ)csc(θ)sec(θ)=csc^2(θ)	prove\:\cot(θ)\csc(θ)\sec(θ)=\csc^{2}(θ)
verificar tan(x)=(2tan(x/2))/(1-tan^2(x/2))	prove\:\tan(x)=\frac{2\tan(\frac{x}{2})}{1-\tan^{2}(\frac{x}{2})}
verificar 1/(sec^2(x))+1/(csc^2(x))-1=0	prove\:\frac{1}{\sec^{2}(x)}+\frac{1}{\csc^{2}(x)}-1=0
verificar 4sin(x)cos(x)cos(2x)=sin(4x)	prove\:4\sin(x)\cos(x)\cos(2x)=\sin(4x)
verificar (sin(x)-cos(x))^2-1=-2sin(x)cos(x)	prove\:(\sin(x)-\cos(x))^{2}-1=-2\sin(x)\cos(x)
verificar-2tan^2(0)=2tan(0)	prove\:-2\tan^{2}(0)=2\tan(0)
verificar 2cot(x)sin(x)=2cos(x)	prove\:2\cot(x)\sin(x)=2\cos(x)
verificar csc^2(x)(sin^2(x)-1)=-cot^2(x)	prove\:\csc^{2}(x)(\sin^{2}(x)-1)=-\cot^{2}(x)
verificar cos(3x)=cos(x)(4cos^2(x)-3)	prove\:\cos(3x)=\cos(x)(4\cos^{2}(x)-3)
verificar 1/(sin(x)cot(x))=sec(x)	prove\:\frac{1}{\sin(x)\cot(x)}=\sec(x)
verificar csc(θ)+sin(θ)=(2-cos^2(θ))/(sin(θ))	prove\:\csc(θ)+\sin(θ)=\frac{2-\cos^{2}(θ)}{\sin(θ)}
verificar cos^2(x)=1-sin(x)cos(x)tan(x)	prove\:\cos^{2}(x)=1-\sin(x)\cdot\:\cos(x)\cdot\:\tan(x)

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