Simplify `(sin theta-cos theta)/(sin thetacos theta)`

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

Simplify: (sin8 theta cos theta-sin6 theta cos3 theta)/(cos2 theta cos theta-sin3 theta sin4 theta)

Simplify sin^8theta-cos^8theta

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

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

(i) |(cos theta,-sin theta),(sin theta,cos theta)|

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

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