`(sin^3theta+cos^3theta)/(sintheta+costheta) + (cos^3theta-sin^3theta)/(costheta-sintheta)` = ?

Prove that (cos^3theta+sin^3 theta)/(cos theta+sin theta)+(cos^3 theta-sin^3 theta)/(cos theta-sin theta)=2

Prove that: (sin2theta)/(costheta cos3theta)+(sin4theta)/(cos3theta.cos5theta)+(sin6theta)/(cos5theta.cos7theta)+… to terms = 1/(2sintheta) [sec(2n+1)theta-sectheta]

(sin^3theta-cos^3theta)/(sintheta-costheta)-(costheta)/(sqrt(1+cot^2theta))-2tanthetacottheta=-1 if theta in (0,pi/2) (b) theta in (pi/2,pi) theta in (pi,(3pi)/2) (d) theta in ((3pi)/2,2pi)

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

If int(sintheta-costheta)/((sintheta+costheta)sqrt(sinthetacostheta+sin^(2)thetacos^(2)theta))d theta = "cosec"^(_1)(f(theta))+C , then

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

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

Prove that sin^(3)theta+cos^(3)theta=(sintheta+costheta)(1-sin thetacostheta) .

Solve: sin2theta+sin4theta=costheta+cos3theta

Evaluate: intcos2thetaln((costheta+sintheta)/(costheta-sin theta))d theta