To prove `(1/(sec^2alpha-cos^2alpha)+1/(cosec^2alpha-sin^2alpha))cos^2alphasin^2alpha=(1-sin^2alphacos^2alpha)/(2+sin^2alphacos^2alpha)`

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

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

If A=[(cos^2 alpha,sin^2alpha),(cos alpha,sin alpha)] and B=[(sin^2 alpha,cos^2 alpha),(sin alpha,cos alpha)]. Find (A+B).

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

if A,=[[cos alpha,sin alpha-sin alpha,cos alphasin alpha,cos alphacos2 alpha,sin2 alpha-sin2 alpha,cos2 alpha]]

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

Prove that, (sin alpha + cos alpha)/(cos alpha-sin alpha)=tan2 alpha + sec 2 alpha

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

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

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