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

Prove the following ((1+cottheta+tantheta)(sintheta-costheta))/(sec^3theta-cosec^3theta)=sin^2thetacos^2theta

Prove that (frac(sintheta-2sin^3theta)(2cos^3theta-costheta))=tantheta

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

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

(tantheta + sintheta)/(tantheta - sintheta) =(sectheta + 1 )/ (sectheta -1)

prove that cot theta + tan theta = cosec theta. Sec theta

Prove that: cot theta + tan theta = cosec theta sec theta .

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

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

(sintheta+sin 2theta)/(1+costheta+cos2theta)=