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

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

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

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

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

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

Prove that: (i) (1+"sin" 2theta-cos 2theta)/(1+"sin" 2theta+cos 2theta)="tan" theta . (ii) 2 tan 2x=(cos x+"sin" x)/(cos x-"sin" x)-(cos x-"sin" x)/(cos x+"sin" x) .

(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 : (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))