`inttan^5thetasec^4d theta`

Prove: sec^6theta=tan^6theta+3tan^2thetasec^2theta+1

int_0^(pi/2) sqrt(sintheta)cos^5theta d theta

Check whether the following equation tan^(4)theta+tan^(6)theta=tan^(3)thetasec^(2)theta is an identity or not ?

I=inttan^(2)(2theta)d""theta is equal to

inttan^mxsec^4xdx

inttan^3xsec^2xdx

inttan^2xdx

Prove: cos e c^2theta+sec^2theta=cos e c^2thetasec^2theta

If tan\ theta/2=(cosec theta-sin theta), then tan^2\ theta/2 may be equal to (A) 2-sqrt(5) (B) (9-4sqrt(5))(2+sqrt(5)) (C) -2+sqrt(5) (D) (9-4sqrt(5))(2-sqrt(5))

int_0^(pi/4) (2sinthetacostheta)/(sin^4theta+cos^4theta)d theta