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Problemas populares de Trigonometría

verificar (1-cos(2x))/(csc(x))=2sin^3(x)	prove\:\frac{1-\cos(2x)}{\csc(x)}=2\sin^{3}(x)
verificar (1+sin(x))^2+cos^2(x)=2(1+sin(x))	prove\:(1+\sin(x))^{2}+\cos^{2}(x)=2(1+\sin(x))
verificar (2-sec^2(x))/(sec^2(x))=cos(2x)	prove\:\frac{2-\sec^{2}(x)}{\sec^{2}(x)}=\cos(2x)
verificar (cos(β))/(1-sin(β))=sec(β)+tan(β)	prove\:\frac{\cos(β)}{1-\sin(β)}=\sec(β)+\tan(β)
verificar csc^2(x)=(tan^2(x)+1)/(tan^2(x))	prove\:\csc^{2}(x)=\frac{\tan^{2}(x)+1}{\tan^{2}(x)}
verificar 2cot(2θ)=cot(θ)-tan(θ)	prove\:2\cot(2θ)=\cot(θ)-\tan(θ)
verificar 7cos^2(b)-7sin^2(b)=14cos^2(b)-7	prove\:7\cos^{2}(b)-7\sin^{2}(b)=14\cos^{2}(b)-7
verificar 1+tan(x)*tan(2x)=sec(2x)	prove\:1+\tan(x)\cdot\:\tan(2x)=\sec(2x)
verificar 0sec(0)=tan(0)	prove\:0\sec(0)=\tan(0)
verificar tan^3(x)(csc^3(x))=sec^3(x)	prove\:\tan^{3}(x)(\csc^{3}(x))=\sec^{3}(x)
verificar sin(x)sec(x)=sin(x)	prove\:\sin(x)\sec(x)=\sin(x)
verificar tan^2(y)-sin^2(y)=tan^2(y)sin^2(y)	prove\:\tan^{2}(y)-\sin^{2}(y)=\tan^{2}(y)\sin^{2}(y)
verificar sin(θ)(1+cot^2(θ))=csc(θ)	prove\:\sin(θ)(1+\cot^{2}(θ))=\csc(θ)
verificar csc(x)-sin(x)=csc(x)cot(x)	prove\:\csc(x)-\sin(x)=\csc(x)\cot(x)
verificar 5+cot^2(x)=4+csc^2(x)	prove\:5+\cot^{2}(x)=4+\csc^{2}(x)
verificar 1/2 sin(2x)=(tan(x))/(1+tan^2(x))	prove\:\frac{1}{2}\sin(2x)=\frac{\tan(x)}{1+\tan^{2}(x)}
verificar sin^2(2x)=(1-cos(4x))/2	prove\:\sin^{2}(2x)=\frac{1-\cos(4x)}{2}
verificar cot(2θ)=(csc(θ)-2sin(θ))/(2cos(θ))	prove\:\cot(2θ)=\frac{\csc(θ)-2\sin(θ)}{2\cos(θ)}
verificar sin^2(θ)sec^2(θ)csc^2(θ)=sec^2(θ)	prove\:\sin^{2}(θ)\sec^{2}(θ)\csc^{2}(θ)=\sec^{2}(θ)
verificar (csc(θ)-sin(θ))/(sin(θ))=cot^2(θ)	prove\:\frac{\csc(θ)-\sin(θ)}{\sin(θ)}=\cot^{2}(θ)
verificar (csc^2(x))/(cot(x))=sec(x)csc(x)	prove\:\frac{\csc^{2}(x)}{\cot(x)}=\sec(x)\csc(x)
verificar csc(x)sin(x)=1	prove\:\csc(x)\sin(x)=1
verificar (sin(x)+cos(x))^2=1-sin(2x)	prove\:(\sin(x)+\cos(x))^{2}=1-\sin(2x)
verificar (cos(A))/(1+sin(A))+(cos(A))/(1-sin(A))=2sec(A)	prove\:\frac{\cos(A)}{1+\sin(A)}+\frac{\cos(A)}{1-\sin(A)}=2\sec(A)
verificar 1/(sin(θ)cos(θ))-1/(tan(θ))=tan(θ)	prove\:\frac{1}{\sin(θ)\cos(θ)}-\frac{1}{\tan(θ)}=\tan(θ)
verificar 6sin(pi/6)=2+2sin(pi/6)	prove\:6\sin(\frac{π}{6})=2+2\sin(\frac{π}{6})
verificar (cos(x+y))/(cos(x-y))=(1-tan(x)tan(y))/(1+tan(x)tan(y))	prove\:\frac{\cos(x+y)}{\cos(x-y)}=\frac{1-\tan(x)\tan(y)}{1+\tan(x)\tan(y)}
verificar cot(x/2)=(sin(x))/(1-cos(x))	prove\:\cot(\frac{x}{2})=\frac{\sin(x)}{1-\cos(x)}
verificar cos^4(x)-sin^4(x)+1=2cos^2(x)	prove\:\cos^{4}(x)-\sin^{4}(x)+1=2\cos^{2}(x)
verificar sin(x)cos(x)=(sin(2x))/2	prove\:\sin(x)\cos(x)=\frac{\sin(2x)}{2}
verificar-tan(y)+sec(y)=(cos(y))/(1+sin(y))	prove\:-\tan(y)+\sec(y)=\frac{\cos(y)}{1+\sin(y)}
verificar 1-(cos^2(θ))/(1-sin(θ))=-sin(θ)	prove\:1-\frac{\cos^{2}(θ)}{1-\sin(θ)}=-\sin(θ)
verificar sin(2z)=2sin(z)cos(z)	prove\:\sin(2z)=2\sin(z)\cos(z)
verificar csc^2(a)sec^2(a)=sec^2(a)+csc^2(a)	prove\:\csc^{2}(a)\sec^{2}(a)=\sec^{2}(a)+\csc^{2}(a)
verificar (sin^2(x))(1+cot^2(x))=1	prove\:(\sin^{2}(x))(1+\cot^{2}(x))=1
verificar cot(x/2)=((1+cos(x)))/(sin(x))	prove\:\cot(\frac{x}{2})=\frac{(1+\cos(x))}{\sin(x)}
verificar 1/(tan(b))+tan(b)=sec(b)csc(b)	prove\:\frac{1}{\tan(b)}+\tan(b)=\sec(b)\csc(b)
verificar csc^2(x)cot^2(x)+csc^2(x)=csc^4(x)	prove\:\csc^{2}(x)\cot^{2}(x)+\csc^{2}(x)=\csc^{4}(x)
verificar sin^5(x)=(sin(x))^5	prove\:\sin^{5}(x)=(\sin(x))^{5}
verificar 2tan(x)sec(x)csc(x)=2+2tan^2(x)	prove\:2\tan(x)\sec(x)\csc(x)=2+2\tan^{2}(x)
verificar (csc^2(x))/(cot^2(x))=csc(x)sec(x)	prove\:\frac{\csc^{2}(x)}{\cot^{2}(x)}=\csc(x)\sec(x)
verificar sin^2(b)csc^2(b)-sin^2(b)=cos^2(b)	prove\:\sin^{2}(b)\csc^{2}(b)-\sin^{2}(b)=\cos^{2}(b)
verificar (tan(θ)+sec(θ))(1-sin(θ))=cos(θ)	prove\:(\tan(θ)+\sec(θ))(1-\sin(θ))=\cos(θ)
verificar cot(pi-x)=-cot(x)	prove\:\cot(π-x)=-\cot(x)
verificar sin(θ)cos(θ)+sin^3(θ)sec(θ)=tan(θ)	prove\:\sin(θ)\cos(θ)+\sin^{3}(θ)\sec(θ)=\tan(θ)
verificar tan(A)sin(A)=sec(A)-cos(A)	prove\:\tan(A)\sin(A)=\sec(A)-\cos(A)
verificar 1/(sin(x))=sin(x)+cos(x)cot(x)	prove\:\frac{1}{\sin(x)}=\sin(x)+\cos(x)\cot(x)
verificar sin(x)sec(x)=1	prove\:\sin(x)\sec(x)=1
verificar sec^2(x)sin^2(x)=sec^2(x)-1	prove\:\sec^{2}(x)\sin^{2}(x)=\sec^{2}(x)-1
verificar tan(a-b)=sin(a-b)sec(a-b)	prove\:\tan(a-b)=\sin(a-b)\sec(a-b)
verificar (csc(B))/(tan(B)+cot(B))=cos(B)	prove\:\frac{\csc(B)}{\tan(B)+\cot(B)}=\cos(B)
verificar sin^2(x+xy)+cos^2(x+xy)=1	prove\:\sin^{2}(x+xy)+\cos^{2}(x+xy)=1
verificar 1/(csc^2(θ))=cos^2(θ)+1	prove\:\frac{1}{\csc^{2}(θ)}=\cos^{2}(θ)+1
verificar sin((17pi)/2+x)=cos(x)	prove\:\sin(\frac{17π}{2}+x)=\cos(x)
verificar (cos^2(θ))/(1+sin(θ))=1-sin(θ)	prove\:\frac{\cos^{2}(θ)}{1+\sin(θ)}=1-\sin(θ)
verificar 4sin(3θ)=12sin(θ)-16sin^3(θ)	prove\:4\sin(3θ)=12\sin(θ)-16\sin^{3}(θ)
verificar tan^2(x)+1/(sin(x)csc(x))=sec^2(x)	prove\:\tan^{2}(x)+\frac{1}{\sin(x)\csc(x)}=\sec^{2}(x)
verificar csc(-x)-sin(-x)=cos(-x)cot(-x)	prove\:\csc(-x)-\sin(-x)=\cos(-x)\cot(-x)
verificar (csc(x))(tan(x))=sec(x)	prove\:(\csc(x))(\tan(x))=\sec(x)
verificar cot(x/2)=(1+cos(x))/(sin(x))	prove\:\cot(\frac{x}{2})=\frac{1+\cos(x)}{\sin(x)}
verificar (sin(x))(csc(x))=1	prove\:(\sin(x))(\csc(x))=1
verificar 1+cos(2t)=cot(t)sin(2t)	prove\:1+\cos(2t)=\cot(t)\sin(2t)
verificar sin(α)=(2tan(α/2))/(1+tan^2(α/2))	prove\:\sin(α)=\frac{2\tan(\frac{α}{2})}{1+\tan^{2}(\frac{α}{2})}
verificar (1+sin(x))(1-sin(x))= 1/(sec^2(x))	prove\:(1+\sin(x))(1-\sin(x))=\frac{1}{\sec^{2}(x)}
verificar sin(3x)cos(2x)-cos(3x)sin(2x)=sin(x)	prove\:\sin(3x)\cos(2x)-\cos(3x)\sin(2x)=\sin(x)
verificar 4cot^2(y)(sec^2(y)-1)=4	prove\:4\cot^{2}(y)(\sec^{2}(y)-1)=4
verificar cos^2(2x)=1-sin^2(2x)	prove\:\cos^{2}(2x)=1-\sin^{2}(2x)
verificar sin^2(x)sec(x)=(sin(x))/(cot(x))	prove\:\sin^{2}(x)\sec(x)=\frac{\sin(x)}{\cot(x)}
verificar cot^2(x)(1+tan^2(x))=csc^2(x)	prove\:\cot^{2}(x)(1+\tan^{2}(x))=\csc^{2}(x)
verificar (sec^2(a)cot(a))/(csc^2(a))=tan(a)	prove\:\frac{\sec^{2}(a)\cot(a)}{\csc^{2}(a)}=\tan(a)
verificar (1-sec(x))/(tan(x))-(tan(x))/(1-sec(x))=2cot(x)	prove\:\frac{1-\sec(x)}{\tan(x)}-\frac{\tan(x)}{1-\sec(x)}=2\cot(x)
verificar (cos(x)sin(x))/(tan(x))=1-sin^2(x)	prove\:\frac{\cos(x)\sin(x)}{\tan(x)}=1-\sin^{2}(x)
verificar sec(x)=sin(x)(cot(x)+tan(x))	prove\:\sec(x)=\sin(x)(\cot(x)+\tan(x))
verificar (cos(x))/(sec(x))=cos^2(x)	prove\:\frac{\cos(x)}{\sec(x)}=\cos^{2}(x)
verificar (3sin(θ)+3cos(θ))^2=9+9sin(2θ)	prove\:(3\sin(θ)+3\cos(θ))^{2}=9+9\sin(2θ)
verificar tan(x)-(sec^2(x))/(tan(x))=-cot(x)	prove\:\tan(x)-\frac{\sec^{2}(x)}{\tan(x)}=-\cot(x)
verificar (tan^2(θ)+1)/(tan^2(θ))=csc^2(θ)	prove\:\frac{\tan^{2}(θ)+1}{\tan^{2}(θ)}=\csc^{2}(θ)
verificar sec^2(x)csc^2(x)-sec^2(x)=csc^2(x)	prove\:\sec^{2}(x)\csc^{2}(x)-\sec^{2}(x)=\csc^{2}(x)
verificar (sec(A)-cos(A))/(csc(A)-sin(A))=tan^3(A)	prove\:\frac{\sec(A)-\cos(A)}{\csc(A)-\sin(A)}=\tan^{3}(A)
verificar (8sin^2(t))/(tan^2(t))=8cos^2(t)	prove\:\frac{8\sin^{2}(t)}{\tan^{2}(t)}=8\cos^{2}(t)
verificar (sin(θ)+sin(3θ))/(2cos(θ))=sin(2θ)	prove\:\frac{\sin(θ)+\sin(3θ)}{2\cos(θ)}=\sin(2θ)
verificar cos(4θ)-4cos(2θ)=8sin^4(θ)-3	prove\:\cos(4θ)-4\cos(2θ)=8\sin^{4}(θ)-3
verificar tan^2(θ)= 1/(cos^2(θ))-1	prove\:\tan^{2}(θ)=\frac{1}{\cos^{2}(θ)}-1
verificar sin(x)cos(x)tan(x)=1-cos^2(x)	prove\:\sin(x)\cos(x)\tan(x)=1-\cos^{2}(x)
verificar (1+tan(u))/(1+cot(u))=tan(u)	prove\:\frac{1+\tan(u)}{1+\cot(u)}=\tan(u)
verificar sec^2(B)= 1/(1-sin^2(B))	prove\:\sec^{2}(B)=\frac{1}{1-\sin^{2}(B)}
verificar 3sin^2(2x)=12cos^2(x)sin^2(x)	prove\:3\sin^{2}(2x)=12\cos^{2}(x)\sin^{2}(x)
verificar cos(θ)=sin(θ)cot(θ)	prove\:\cos(θ)=\sin(θ)\cot(θ)
verificar sin(θ)cos(θ)=1	prove\:\sin(θ)\cos(θ)=1
verificar (cos(x)+sin(x))^2=1+sin(2x)	prove\:(\cos(x)+\sin(x))^{2}=1+\sin(2x)
verificar csc(θ)-csc(θ)cos^2(θ)=sin(θ)	prove\:\csc(θ)-\csc(θ)\cos^{2}(θ)=\sin(θ)
verificar (sin(6x)+sin(2x))/(cos(6x)+cos(2x))=tan(4x)	prove\:\frac{\sin(6x)+\sin(2x)}{\cos(6x)+\cos(2x)}=\tan(4x)
verificar sec^2(a)=1+tan^2(a)	prove\:\sec^{2}(a)=1+\tan^{2}(a)
verificar (tan(θ))/(csc(θ))=sec(θ)-cos(θ)	prove\:\frac{\tan(θ)}{\csc(θ)}=\sec(θ)-\cos(θ)
verificar cot(2β)=(cot^2(β)-1)/(2cot(β))	prove\:\cot(2β)=\frac{\cot^{2}(β)-1}{2\cot(β)}
verificar (2sin(x)-2cos(x))^2=4-4sin(2x)	prove\:(2\sin(x)-2\cos(x))^{2}=4-4\sin(2x)
verificar csc^2(y)tan^2(y)-1=tan^2(y)	prove\:\csc^{2}(y)\tan^{2}(y)-1=\tan^{2}(y)
verificar cot(θ)tan(θ)=1	prove\:\cot(θ)\tan(θ)=1
verificar 4cos^2(x)-2=-1	prove\:4\cos^{2}(x)-2=-1
verificar cot(2x)= 1/2 (cot(x)-tan(x))	prove\:\cot(2x)=\frac{1}{2}(\cot(x)-\tan(x))

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