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

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

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

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

Prove the following: (frac(tantheta+sectheta-1)(tantheta+sectheta+1))=(frac(tantheta)(sectheta+1))

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

Prove the following identities: (frac(1-sectheta+tantheta)(1+sectheta-tantheta))=(frac(sectheta+tantheta-1)(sectheta+tantheta+1))

Prove the following identities: (frac(1)(sectheta+tantheta))-(frac(1)(costheta))=(frac(1)(costheta))-(frac(1)(sectheta-tantheta))

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

Solve the following:Prove that (frac(cos^3theta-cos3theta)(costheta))+(frac(sin^3theta+sin3theta)(sintheta))=3

sintheta/(1-cottheta)+costheta/(1-tantheta)=