Simplify `(1-costheta)^2/sin^2theta`

Simplify cos^2theta-sin^2theta

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

Simplify [(sin theta)/(cos theta)+(cos theta)/(sin theta)]^(2)

Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

Prove that : (sintheta-costheta)/(sintheta+costheta)+(sintheta+costheta)/(sintheta-costheta)=(2)/(2sin^(2)theta-1)

Simplify sqrt(1- sin^2theta ) + (1 cos^2theta)

If 0^(@)lethetale90^(@) , then solve the following equations : (i) (costheta)/(1-sintheta)+(costheta)/(1+sintheta)=4 (ii) (cos^(2)theta-3costheta+2)/(sin^(2)theta)=1 (iii) (costheta)/("cosec"theta+1)+(costheta)/("cosec"theta-1)=2

costheta-cos2theta=sin3theta

The integral I=intsin (2theta)[(1+cos^(2)theta)/(2sin^(2)theta)]d theta simplifies to (where, c is the integration constant)