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

The value of the integral int_(0)^(pi//4) (sin theta+cos theta)/(9+16 sin 2theta)d theta , is

int_0^(pi/4)sectheta d theta =

Prove the following identities: 2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1=0 sin^6theta+cos^6theta+3sin^2thetacos^2theta=1 (sin^8theta-cos^8theta)=(sin^2theta-cos^2theta)(1-2s in^2thetacos^2theta)

6) int_0^(pi/4)sec^4theta d theta

6) int_0^(pi/4)sec^4theta d theta

5. int_0^(pi/4)sec^2theta d theta

Evaluate: int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2thetad theta .

Evaluate: int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2thetad theta

2(sin^(6) theta + cos^(6)theta) - 3(sin^(4)theta + cos^(4)theta)+ 1 = 0

4(sin^(6)theta+cos^(6)theta)-6(sin^(4)theta+cos^(4)theta) is equal to