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Problemas populares de Trigonometría

verificar (1-sec(x))/(csc(x))=cos(x)(cot(x))	prove\:\frac{1-\sec(x)}{\csc(x)}=\cos(x)(\cot(x))
verificar cos(piθ)=-cos(θ)	prove\:\cos(πθ)=-\cos(θ)
verificar csc(x)tan(x)sec(x)=sec^2(x)	prove\:\csc(x)\tan(x)\sec(x)=\sec^{2}(x)
verificar tan(x)sec^4(x)=(sin(x))/(cos^5(x))	prove\:\tan(x)\sec^{4}(x)=\frac{\sin(x)}{\cos^{5}(x)}
verificar csc(x)+cot(x)sec(x)-1=tan(x)	prove\:\csc(x)+\cot(x)\sec(x)-1=\tan(x)
verificar (3csc(x)-3sin(x))/(tan(x)-cot(x))=3cos^3(x)	prove\:\frac{3\csc(x)-3\sin(x)}{\tan(x)-\cot(x)}=3\cos^{3}(x)
verificar 9cos(x)+6sin(x)=10	prove\:9\cos(x^{\circ\:})+6\sin(x^{\circ\:})=10
verificar (tan^2(A))/(sec^2(A))=sin^2(A)	prove\:\frac{\tan^{2}(A)}{\sec^{2}(A)}=\sin^{2}(A)
verificar sin(2x)-cot(x)=cot(x)cos(2x)	prove\:\sin(2x)-\cot(x)=\cot(x)\cos(2x)
verificar tan(x)+cot(x)*tan(x)=sec^2(x)	prove\:\tan(x)+\cot(x)\cdot\:\tan(x)=\sec^{2}(x)
verificar sin(4θ)= 3/8-cos(2θ)+1/8 cos(4θ)	prove\:\sin(4θ)=\frac{3}{8}-\cos(2θ)+\frac{1}{8}\cos(4θ)
verificar 5cos^2(x)-2cos(x)-3-sin^2(x)=0	prove\:5\cos^{2}(x)-2\cos(x)-3-\sin^{2}(x)=0
verificar sin(x)cos(pi/6)-cos(x)sin(pi/6)=sin(x-pi/6)	prove\:\sin(x)\cos(\frac{π}{6})-\cos(x)\sin(\frac{π}{6})=\sin(x-\frac{π}{6})
verificar cos^4(a)+1-sin^4(a)=2cos^2(a)	prove\:\cos^{4}(a)+1-\sin^{4}(a)=2\cos^{2}(a)
verificar 3-4cos^2(x)=(2sin(x)+1)(2sin(x)-1)	prove\:3-4\cos^{2}(x)=(2\sin(x)+1)(2\sin(x)-1)
verificar csc^2(θ)=(1/(sin(θ)))^2	prove\:\csc^{2}(θ)=(\frac{1}{\sin(θ)})^{2}
verificar (1+tan(x))/(1+1/(tan(x)))=tan(x)	prove\:\frac{1+\tan(x)}{1+\frac{1}{\tan(x)}}=\tan(x)
verificar cos(2θ)= 1/(sec(2θ))	prove\:\cos(2θ)=\frac{1}{\sec(2θ)}
verificar 1/(csc^2(A))+1/(cot^2(A))=1	prove\:\frac{1}{\csc^{2}(A)}+\frac{1}{\cot^{2}(A)}=1
verificar (cos(3x)-cos(x))=-2sin(2x)sin(x)	prove\:(\cos(3x)-\cos(x))=-2\sin(2x)\sin(x)
verificar sec(pi/2-y)=csc(y)	prove\:\sec(\frac{π}{2}-y)=\csc(y)
verificar cos(2x-pi/2)=cos(pi/2-2x)	prove\:\cos(2x-\frac{π}{2})=\cos(\frac{π}{2}-2x)
verificar sin(pi/2-x)cot(pi/2+x)=-sin(x)	prove\:\sin(\frac{π}{2}-x)\cot(\frac{π}{2}+x)=-\sin(x)
verificar cos(x)csc(x)tan(x)=1	prove\:\cos(x)\cdot\:\csc(x)\cdot\:\tan(x)=1
verificar-2sin(2(x+45))=2cos(2x)	prove\:-2\sin(2(x+45))=2\cos(2x)
verificar cos^2(x) 1/(cos^2(x))=1	prove\:\cos^{2}(x)\frac{1}{\cos^{2}(x)}=1
verificar (sin((4pi)/3))=-(sqrt(3))/2	prove\:(\sin(\frac{4π}{3}))=-\frac{\sqrt{3}}{2}
verificar sec(x)-sin^2(x)=cos(x)	prove\:\sec(x)-\sin^{2}(x)=\cos(x)
verificar cot^2(x)=csc^2(x)(1-sin^2(x))	prove\:\cot^{2}(x)=\csc^{2}(x)(1-\sin^{2}(x))
verificar sec(x)-(tan^2(x))/(sec(x))=cos(x)	prove\:\sec(x)-\frac{\tan^{2}(x)}{\sec(x)}=\cos(x)
verificar (cos(2θ))/(-sin^2(θ))=cos^2(θ)	prove\:\frac{\cos(2θ)}{-\sin^{2}(θ)}=\cos^{2}(θ)
verificar 1/(cos^3(x))=sec^3(x)	prove\:\frac{1}{\cos^{3}(x)}=\sec^{3}(x)
verificar sin(x)+cot(x)(cos(x))=csc(x)	prove\:\sin(x)+\cot(x)(\cos(x))=\csc(x)
verificar 1/(csc(x)-1)=(sin(x))/1	prove\:\frac{1}{\csc(x)-1}=\frac{\sin(x)}{1}
verificar (1-(cos(x)))/(sec(x)-1)=cos(x)	prove\:\frac{1-(\cos(x))}{\sec(x)-1}=\cos(x)
verificar sec(θ)cos(θ)csc(θ)=cot(θ)	prove\:\sec(θ)\cos(θ)\csc(θ)=\cot(θ)
verificar cot(x)(sin(x)+tan(x))=1+cos(x)	prove\:\cot(x)(\sin(x)+\tan(x))=1+\cos(x)
verificar csc^2(x)(1-cos^2(x))=tan(420)	prove\:\csc^{2}(x)(1-\cos^{2}(x))=\tan(420^{\circ\:})
verificar 1-cot(x)=1	prove\:1-\cot(x)=1
verificar cot(x)-csc(x)=-1/(cot(x)+csc(x))	prove\:\cot(x)-\csc(x)=-\frac{1}{\cot(x)+\csc(x)}
verificar cos(θ+30)-sin(θ+60)=-sin(θ)	prove\:\cos(θ+30^{\circ\:})-\sin(θ+60^{\circ\:})=-\sin(θ)
verificar (tan^2(x))/(sec(x))=sin(tan(x))	prove\:\frac{\tan^{2}(x)}{\sec(x)}=\sin(\tan(x))
verificar sin^2(0)=2-2cos(0)	prove\:\sin^{2}(0)=2-2\cos(0)
verificar cos((3pi)/8)=(sqrt(2-\sqrt{2)})/2	prove\:\cos(\frac{3π}{8})=\frac{\sqrt{2-\sqrt{2}}}{2}
verificar tan(a)*cot(a)=sin^2(a)+cos^2(a)	prove\:\tan(a)\cdot\:\cot(a)=\sin^{2}(a)+\cos^{2}(a)
verificar tan(x)+(cos(x))/(1-sin(x))=sec(x)	prove\:\tan(x)+\frac{\cos(x)}{1-\sin(x)}=\sec(x)
verificar sin(x)cos(x)=tan(x)	prove\:\sin(x)\cos(x)=\tan(x)
verificar cot((15pi)/8)=cot((7pi)/8)	prove\:\cot(\frac{15π}{8})=\cot(\frac{7π}{8})
verificar 7-sin(x)=1-(cos^2(x))/(1-sin(x))	prove\:7-\sin(x)=1-\frac{\cos^{2}(x)}{1-\sin(x)}
verificar 1/(csc^2(x))=1-sin^2(x)	prove\:\frac{1}{\csc^{2}(x)}=1-\sin^{2}(x)
verificar sin^4(x)=(sin^2(x))^2	prove\:\sin^{4}(x)=(\sin^{2}(x))^{2}
verificar sin(2x)-cos(2x)= 1/2	prove\:\sin(2x)-\cos(2x)=\frac{1}{2}
verificar (cot(α))/(cos(α))=csc(α)	prove\:\frac{\cot(α)}{\cos(α)}=\csc(α)
verificar cos^{(2)}(θ)(1+tan^{(2)}(θ))=1	prove\:\cos^{(2)}(θ)(1+\tan^{(2)}(θ))=1
verificar 1-2sin^2(y)+sin^4(y)=cos^4(y)	prove\:1-2\sin^{2}(y)+\sin^{4}(y)=\cos^{4}(y)
verificar (sin(x)+cos(x))^2-2sin(x)cos(x)=1	prove\:(\sin(x)+\cos(x))^{2}-2\sin(x)\cos(x)=1
verificar (cos(θ))/(sin^2(θ))=2cos^2(θ)	prove\:\frac{\cos(θ)}{\sin^{2}(θ)}=2\cos^{2}(θ)
verificar (1-sin(3a))(sin(3a)+1)=cos^2(3a)	prove\:(1-\sin(3a))(\sin(3a)+1)=\cos^{2}(3a)
verificar (sin(x))/(1+cos(2x))=tan(x)	prove\:\frac{\sin(x)}{1+\cos(2x)}=\tan(x)
verificar cos^2(((12pi))/2)=cos^2(12pi)	prove\:\cos^{2}(\frac{(12π)}{2})=\cos^{2}(12π)
verificar sin^2(x)= 1/2-cos(2x) 1/2	prove\:\sin^{2}(x)=\frac{1}{2}-\cos(2x)\frac{1}{2}
verificar sec(t)(csc(t)(tan(t)+cot(t)))=sec^2(t)+csc^2(t)	prove\:\sec(t)(\csc(t)(\tan(t)+\cot(t)))=\sec^{2}(t)+\csc^{2}(t)
verificar (1+sin(x))^2+cos^2(x)=2+2sin(x)	prove\:(1+\sin(x))^{2}+\cos^{2}(x)=2+2\sin(x)
verificar tan(x)*(1+cos(2x))=sin(2x)	prove\:\tan(x)\cdot\:(1+\cos(2x))=\sin(2x)
verificar 2sin^2(x)+sin(x)=0	prove\:2\sin^{2}(x)+\sin(x)=0
verificar cot(60)=(cos(60))/(sin(60))	prove\:\cot(60^{\circ\:})=\frac{\cos(60^{\circ\:})}{\sin(60^{\circ\:})}
verificar (sec(x))/(cos(x))=sec^2(x)	prove\:\frac{\sec(x)}{\cos(x)}=\sec^{2}(x)
verificar tan(-x)tan(pi/2-x)=-1	prove\:\tan(-x)\tan(\frac{π}{2}-x)=-1
verificar tan(z)cos(z)csc(z)=1	prove\:\tan(z)\cdot\:\cos(z)\cdot\:\csc(z)=1
verificar tan(pi-θ)=-tan(x)	prove\:\tan(π-θ)=-\tan(x)
verificar cot(θ)(sin(θ)+tan(θ))=cos(θ)+1	prove\:\cot(θ)(\sin(θ)+\tan(θ))=\cos(θ)+1
verificar (2-sin^2(x))csc^2(x)=cot^2(x)	prove\:(2-\sin^{2}(x))\csc^{2}(x)=\cot^{2}(x)
verificar 1/(tan(A))+tan(A)= 2/(sin(2A))	prove\:\frac{1}{\tan(A)}+\tan(A)=\frac{2}{\sin(2A)}
verificar 2sin^2(x)+4cos^2(x)=2-4sin^2(x)	prove\:2\sin^{2}(x)+4\cos^{2}(x)=2-4\sin^{2}(x)
verificar 1+sin(θ)=cos(θ)	prove\:1+\sin(θ)=\cos(θ)
verificar 1+((tan^2(x)))/(1+sec(x))=sec(x)	prove\:1+\frac{(\tan^{2}(x))}{1+\sec(x)}=\sec(x)
verificar (sin(4x))/4 =(sin(x)cos(x))/4	prove\:\frac{\sin(4x)}{4}=\frac{\sin(x)\cos(x)}{4}
verificar csc^2(x)*cos^2(x)=cot^2(x)	prove\:\csc^{2}(x)\cdot\:\cos^{2}(x)=\cot^{2}(x)
verificar 1/(sec^3(x)cos^4(x))=sec(x)	prove\:\frac{1}{\sec^{3}(x)\cos^{4}(x)}=\sec(x)
verificar csc^2(θ)+1=cot^2(θ)	prove\:\csc^{2}(θ)+1=\cot^{2}(θ)
verificar cos(x)sin(x)=(sin(x))/(sec(x))	prove\:\cos(x)\sin(x)=\frac{\sin(x)}{\sec(x)}
verificar-sin^2(θ)=cos^2(θ)	prove\:-\sin^{2}(θ)=\cos^{2}(θ)
verificar sec^2(x)=(cos(x))/(sin(x))	prove\:\sec^{2}(x)=\frac{\cos(x)}{\sin(x)}
verificar sec^2(x)cot^2(x)=cot^2(x)+1	prove\:\sec^{2}(x)\cot^{2}(x)=\cot^{2}(x)+1
verificar 1+tan^2(B)=sec^2(B)	prove\:1+\tan^{2}(B)=\sec^{2}(B)
verificar sec((3pi)/4)=-sqrt(2)	prove\:\sec(\frac{3π}{4})=-\sqrt{2}
verificar cos^2(7θ)-sin^2(7θ)=cos(14θ)	prove\:\cos^{2}(7θ)-\sin^{2}(7θ)=\cos(14θ)
verificar sin^4(x)-(3/(4*sin^2(x)))+1=1	prove\:\sin^{4}(x)-(\frac{3}{4\cdot\:\sin^{2}(x)})+1=1
verificar arccot(x)=tan(x)	prove\:\arccot(x)=\tan(x)
verificar cot(θ)+tan(θ)=sec(θ)+csc(θ)	prove\:\cot(θ)+\tan(θ)=\sec(θ)+\csc(θ)
verificar sin(750)=sin(450+300)	prove\:\sin(750^{\circ\:})=\sin(450^{\circ\:}+300^{\circ\:})
verificar 2sin(θ)+sin(2θ)=0	prove\:2\sin(θ)+\sin(2θ)=0
verificar cos^2(x)+cos(x)-1+sin^2(x)=cos(x)	prove\:\cos^{2}(x)+\cos(x)-1+\sin^{2}(x)=\cos(x)
verificar (2sin(x)cos(x))/(cos(x))=2	prove\:\frac{2\sin(x)\cos(x)}{\cos(x)}=2
verificar tan(x-(3pi)/2)=-cot(x)	prove\:\tan(x-\frac{3π}{2})=-\cot(x)
verificar tan(1/2 x)+cos(1/2 x)=2csc(x)	prove\:\tan(\frac{1}{2}x)+\cos(\frac{1}{2}x)=2\csc(x)
verificar sin(θ)(cos^2(θ))/(sin(θ))=csc(θ)	prove\:\sin(θ)\frac{\cos^{2}(θ)}{\sin(θ)}=\csc(θ)
verificar (tan^2(a)+1)/(sec(a))=sec(a)	prove\:\frac{\tan^{2}(a)+1}{\sec(a)}=\sec(a)
verificar 3sin^2(2x) 1/2 =(3cos(4x))/4	prove\:3\sin^{2}(2x)\frac{1}{2}=\frac{3\cos(4x)}{4}
verificar sin(3x)=3sin(x)cos^2(x)-sin^2(x)	prove\:\sin(3x)=3\sin(x)\cos^{2}(x)-\sin^{2}(x)

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