If `(2+sqrt(3))cos x + sin x = 1` then `theta =`

If 2sin^(2)x + sqrt(3) cos x + 1 =0 , then theta =

If 4sin^(2)x-2 (1+sqrt(3))sin x + sqrt(3)=0 then theta =

If sin theta+sqrt(3)cos theta>=1 then

If x=sqrt(3)(3 sin theta+sin 3theta), y=sqrt(3)(3 sin theta+cos 3 theta) , find (d^(2)y)/(dx^(2)) at theta=(pi)/(3) .

The derivative of the function f(x)=cos^(-1)((1)/(sqrt(13))(2cos x-3sin x))+sin^(-1)((1)/(sqrt(13))(2cos x+3sin x)), with respect to sqrt(1+x^(2)) at x=(3)/(4) is

If (2 sin theta )/(1+ cos theta + sin theta )=x, find the value of (1- cos theta + sin theta )/(1+ sin theta )

If x=sqrt(tan theta)-1 and y=sqrt((cos theta-sin theta)/(sin theta+cos theta)+2 then the value of )(2+2x+x^(2))(5-4y+y^(2)) is

Evaluate the following limits (i) lim_(x to (pi)/(2)) tan^(2) x [sqrt(2 sin^(2) x + 3 sin x + 4) - sqrt(sin^(2) x + 6 sin x + 2)] (ii) lim_(theta to 0) (sqrt(1 + sin 3 theta) -1)/(ln(1 + tan 2theta)) (iii) lim_(x to 0) (sqrt(1 + x) - ""^(3)sqrt(1 + x))/(x) (iv) lim_(phi to 0) (8)/(phi^(8)) (1 - cos (phi^(2))/(2) - cos (phi^(2))/(4) + cos (phi^(2))/(2). cos (phi^(2))/(4))

Evaluate the following limits (i) lim_(x to (pi)/(2)) tan^(2) x [sqrt(2 sin^(2) x + 3 sin x + 4) - sqrt(sin^(2) x + 6 sin x + 2)] (ii) lim_(theta to 0) (sqrt(1 + sin 3 theta) -1)/(ln(1 + tan 2theta)) (iii) lim_(x to 0) (sqrt(1 + x) - ""^(3)sqrt(1 + x))/(x) (iv) lim_(phi to 0) (8)/(phi^(8)) (1 - cos (phi^(2))/(2) - cos (phi^(2))/(4) + cos (phi^(2))/(2). cos (phi^(2))/(4))