The larger of `cos[log(theta)]` and `log(costheta)` if `e^(-pi/2) < theta < pi/ 2` is

Which one is greater: cos(log_e theta)or log_e(costheta) if -pi/2ltthetaltpi/2

The value of sqrt((1+costheta)/(1-costheta)) is (a) cottheta-cos e c\ theta (b) cos e c\ theta+cottheta (c) cos e c^2theta+cot^2theta (d) (cottheta+cos e c\ theta)^2

If cos theta > sin theta > 0, then evaluate : int{log((1+sin2theta)/(1-sin2theta))^(cos^(2) theta)+log((cos2theta)/(1+sin2theta))} d theta

The possible value of theta in [-pi, pi] satisfying the equation 2(costheta + cos 2theta)+ (1+2costheta)sin 2theta = 2sintheta are

The number of solutions of the equation log_(5)tan theta =log_(5)4. log_(4)(3sin theta)"in" [0, 8pi] is

The solution of costheta.cos2theta.cos3theta=1/4,0 lt theta lt pi/4 is:

theta is said to be well behaved if it lies in interval [0,(pi)/(2)]. They are intelligent if they make domain of f +g and g equal. The vlaue of theta for which h (theta) is defined are handosome. Let f (x)= sqrt(thetax ^(2) -2 (theta^(2) -3) x-12theta,) g (x)=ln (x^(2) -49), h (theta) ln [int_(0)^(theta) 4 cos ^(2)t dt - theta ^(2)], where theta is in radians. Complete set of alues of theta which are intelligent is :

The value of the determinant |(sintheta, costheta, sin2theta) , (sin(theta+(2pi)/3), cos(theta+(2pi)/3), sin(2theta+(4pi)/3)) , (sin(theta-(2pi)/3), cos(theta-(2pi)/3), sin(2theta-(4pi)/3))|

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

Prove that: ("cos"(2pi+theta)"c o s e c"(2pi+theta)"tan"(pi//2+theta))/("sec"(pi//2+theta)costheta"cot"(pi+theta))=1