`sqrt(2+sqrt(2+2cos 4 theta)), forall 0 lt theta lt pi//4` is

If alpha and beta are roots of x^(2)-(sqrt(1-cos 2 theta))x+theta=0 , where 0 lt theta lt (pi)/2 . Then lim_(theta to 0^(+))(1/(alpha)+1/(beta)) is

If f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta))) , where -pi/4 lt theta lt pi/4, then the value of d/(d(tantheta))\ f(theta) is

Solve tan theta tan 4theta=1 for 0 lt theta lt pi .

Prove that sqrt ( 2 + sqrt (2 + sqrt (2 + 2 cos 8 theta))) = 2 cos theta, where theta in [ (-pi)/(8), (pi)/(8)]

Prove that 1+cot theta <= cot (theta/2) for 0 < theta < pi . Find theta when equality signs holds.

cot^(2) theta - (1 + sqrt3) cot theta + sqrt3 = 0,0 lt theta lt (pi)/(2)

If cos theta - sin theta = (1)/(5) , where 0 lt theta lt (pi)/(4) , then

if alpha and beta the roots of z+ (1)/(z) =2 (cos theta + I sin theta ) where 0 lt theta lt pi and i=sqrt(-1) show that |alpha - i |= | beta -i|

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

If sin theta =sqrt(3) cos theta, -pi lt theta lt 0 , then the value of theta is