`(1/{sec^2 alpha-cos^2 alpha}+1/{cosec^2 alpha-sin^2 alpha})cos^2 alpha*sin^2 alpha=(1-cos^2alpha*sin^2alpha)/(2+cos^2alpha*sin^2alpha)`

To prove ((1)/(sec^(2)alpha-cos^(2)alpha)+(1)/(cos ec^(2)alpha-sin^(2)alpha))cos^(2)alpha sin^(2)alpha=(1-sin^(2)alpha cos^(2)alpha)/(2+sin^(2)alpha cos^(2)alpha)

sin alpha-sin2 alpha+sin3 alpha=4cos(3 alpha)/(2)cos alpha sin(alpha)/(2)

(cos2 alpha)/(cos^(4)alpha-sin^(4)alpha)-(cos^(4)alpha+sin^(4)alpha)/(2-sin^(2)2 alpha)=

Prove that, (1+ cos 2 alpha + sin 2 alpha)/(1-cos 2 alpha +sin 2 alpha)=cot alpha

(sin alpha)/(1+cos alpha)+(1+cos alpha)/(sin alpha)=2cosec alpha

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

Prove that sin^2alpha-sin^4alpha= cos^2alpha-cos^4alpha

sin alpha+sin2 alpha+sin4 alpha+sin5 alpha=4cos((alpha)/(2))cos(3(alpha)/(2))sin3 alpha

sin alpha+sin2 alpha+sin4 alpha+sin5 alpha=4cos((alpha)/(2))cos(3(alpha)/(2))sin3 alpha