`(sin theta+cos theta)^(2)=1+2sin theta*cos theta`

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

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

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

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

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

(1+sin2 theta-cos2 theta)/(1+sin2 theta+cos2 theta)=tan 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 : (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+1)/(sin theta+cos theta-1)=(1+sin theta)/(cos theta)

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