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)) `

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

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

Prove the following identities: (sin^(3)theta+cos^(3)theta)/(sin theta+cos theta)+sin theta cos theta=1

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

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

Prove each of the following identities : ( cos^(2) theta)/((1- tan theta)) + (sin^(3) theta)/((sin theta - cos theta)) = (1+ sin theta cos theta)

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

(1+sin2 theta-cos2 theta)/(1+sin2 theta+cos2 theta)=tan theta

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