2. `int(1)/(sin^(2)theta*cos^(2)theta)d theta`

The value of f(k)=int_(0)^(pi//2) log (sin ^(2) theta +k^(2) cos^(2) theta) d theta is equal to

If "cosec" theta = sqrt(5) , find the value of (i) 2-sin^(2)theta - cos^(2)theta (ii) 2 + (1)/(sin^(2)theta) - (cos^(2)theta)/(sin^(2)theta)

Let f beintegrable over [0,a] for any real value of a . If I_(1)=int_(0)^(pi//2)cos theta f(sin theta +cos^(2) theta) d theta and I_(2)=int_(0)^(pi//2) sin 2 theta f(sin theta+cos^(2) theta) d theta , then

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

Verify : sin^(2)theta+cos^(2)theta=1" if "theta=30^(@),

The value of int_(0)^(pi//2)(log(1+x sin^(2) theta))/(sin^(2)theta)d theta,xge0 is equal to

Prove that: (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cot theta

Prove that: (a) (sin 2 theta)/(1+cos 2 theta)=tan theta (b) (1+sin 2 theta+cos 2theta)/(1+sin2 theta-cos 2 theta)=cot theta

If (sin^(3)theta-cos^(3)theta)/(sin theta-cos theta)-(cos theta)/(sqrt(1+cot^(2)theta))-2 tan theta cot theta=-1 (AA theta in[0, 2pi], then

The integral I=intsin (2theta)[(1+cos^(2)theta)/(2sin^(2)theta)]d theta simplifies to (where, c is the integration constant)