[30" prove that "],[(sin theta-cos theta)/(sin theta+cos theta)+(sin theta+cos theta)/(sin theta-cos theta)=(2)/(2sin^(2)theta-1)]

Prove that : (1+sin2 theta-cos 2theta)/(sin theta+cos theta)=2sin 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))

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

Prove that (sin theta+cos theta)/(sin theta- cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = ( 2sec^(2) theta)/(tan^(2) theta -1) .

cos theta+sin theta=cos2 theta+sin2 theta

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))

(sin theta-cos theta)^(2)*(sin theta+cos theta)^(2)=

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

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

Prove that (1+cos theta)/(sin theta)=(1+sin theta+cos theta)/(1+sin theta-cos theta) .