If `lim_(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0`,where `theta in (-pi,pi],` then the value of `theta` is (a)`+-pi/4` (b) `+-pi/3` (c) `+-pi/6` (d) `+-pi/2`

If lim_( x to 0) [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) theta, b gt 0 and theta in ( - pi, pi] , then the value of theta is

If theta=sin^(-1){sin(-600o)} , then one of the possible values of theta is pi/3 (b) pi/2 (c) (2pi)/3 (d) (-2pi)/3

If sin^(22)theta+cos^(42)theta=(3)/(4) where theta in[0,(pi)/(2)] then find the sum of all values of theta (a) pi (b) -pi(c)(5 pi)/(4) (d) (pi)/(2)

If (1-tantheta)/(1+tantheta) = 1/sqrt3 , where theta in (0, pi/2) , then theta = (a) pi/6 (b) pi/4 (c) pi/12 (d) pi/3

The period of cos(theta/2) is (A) 2 pi (B) 4 pi (C) pi (D) 6 pi

If tan theta=(1)/(2) andtan varphi =(1)/(3), then the value of theta+varphi is (pi)/(6) (b) pi(c)0(d)(pi)/(4)

If tan^(-1)(cottheta)=2\ theta , then theta= +-pi/3 (b) +-pi/4 (c) +-pi/6 (d) none of these

If (1)/(6)sin theta,cos theta and tan theta are in GP,then the general value of theta is (i) 2n pi+-(pi)/(3)( ii) 2n pi+-(pi)/(6) (iii) 2n pi+-(-1)^(n)(pi)/(3)( iv )n pi+-(pi)/(3)

The sum of all the solutions of cot theta=sin2 theta(theta!=n pi,n integer) 0<=theta<=pi, is (a) (3 pi)/(2) (b) pi (c) 3(pi)/(4) (d) 2 pi