Prove that `(frac(1+sintheta)(1+costheta))`+`(frac(1-sintheta)(1-costheta))`=`2(cosec^2theta-cottheta)`

Prove that (frac(1+sintheta-costheta)(1+sintheta+costheta))=sqrt(1-costheta)/sqrt(1+costheta)

Prove the following identities: (frac(sintheta)(1+costheta))+(frac(1+costheta)(sintheta))=2cosectheta

Prove the following: (frac(sintheta)(1+costheta))=tan(theta/2)

Prove that (frac(1-tantheta)(1-cottheta))^2=tan^2 theta

Prove that : (sin theta)/(1 - costheta) = cosec theta + cot theta

Prove the following: (frac(1+cottheta+cosectheta)(1-cottheta-cosectheta))=(frac(cosectheta+cottheta-1)(cottheta-cosectheta+1))

Prove that ((1+cottheta+tantheta)(sintheta-costheta))=(frac(sectheta)(cosec^2theta))-(frac(cosectheta)(sec^2theta))

Prove the following: (frac(sin^3theta+cos^3theta)(sintheta+costheta))+(frac(sin^3theta-cos^3theta)(sintheta-costheta))=2

Prove that: |(x.sintheta,costheta),(-sintheta,-x,1),(costheta,1,x)|=-x^3

Prove 1/(1+sintheta)+1/(1-sintheta) = 2 sec^2 theta