`(cos theta + sin thetacos theta + costheta - sin thetacos theta)/(1-sin^2theta) = `

sin 4theta=4sin thetacos^3 theta-4costhetasin^3theta

Prove each of the following identities : (sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = (2) /((sin^(2) theta - cos^(2) theta)) = (2) /((2sin^(2) theta -1))

The value of (sin^3 theta + cos^3 theta)/(sin theta+ costheta)+((cos^3 theta - sin^3 theta))/(cos theta - sin theta) is

((sin theta+cos theta)^(2)-1)/(sin theta*cos theta)

cos^(2)theta-sin theta.cos theta-(1)/(2)=0

(1+cos theta+sin theta)/(1+cos theta-sin theta)=(1+sin theta)/(cos theta)

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)

(sin theta+cos theta)(1-sin theta cos theta)=sin^3 theta+cos^3 theta