If `=|s inthetacosvarphisinthetas invarphicosthetacosthetacosvarphicosthetas invarphi-s intheta-s inthetas invarphis inthetacosvarphi0|` then `` is independent of `theta` `` is independent of `varphi` `"Delta"` is a constant `((d"Delta")/(dtheta)])_(theta=pi//2)=0`

The value of tan^(-1)((xcostheta)/(1-xsintheta))-cot^(-1)((costheta)/(x-sintheta))i s 2theta (b) theta (c) theta/2 (d) independent of theta

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

int_0^(pi//2)(theta/sintheta)^2d theta=

If f(theta)=|sinthetacosthetasinthetacosthetasinthetacosthetacosthetasinthetasintheta| , then f(theta)=0 has exactly 2 real solutions in [0,pi] f(theta)=0 has exactly 3 real solutions in [0,pi] range of function (f(theta))/(1-sin2theta)i s[-sqrt(2),sqrt(2)] range of function (f(theta))/(sin2theta-1)i s[-3,3]

Evaluate: int_(-pi/2)^(pi/2)log((a-sin theta)/(a+sin theta)) d theta,a >0

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

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

(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)

Evaluate int_(0)^(pi//2) cos theta tan ^(-1) ( sin theta)d theta .

If f(x)=int_0^(pi/2)ln(1+xsin^2theta)/(sin^2theta) d theta, x >= 0 then :