If `(pi)/(2)ltalphalt(2pi)/(3)andl=int_(0)^(sin2alpha)(dx)/(sqrt(4cos^(2)alpha-x^(2)))`, then the value of `(l+alpha)/(pi)` must be__________.

If (pi)/(2)lt alpha lt (3pi)/(4) , then sqrt(2tan alpha+(1)/(cos^(2)alpha)) is equal to

If alpha in [-2pi, 2pi] and cos.(alpha)/(2)+sin.(alpha)/(2)=sqrt(2)(cos 36^(@)-sin18^(@)) , then a value of alpha

If (sin alpha)^(x)+(cos alpha)^(x) ge 1,0 lt a lt (pi)/(2) then

If sin alpha=-3/6, alpha in [0,2pi] then the possible values of cos (alpha/2) , is/are

Evaluate int_(0)^(pi)(x dx)/(1+cos alpha sin x) ,where 0lt alpha lt pi .

If alpha, betaepsilon(0, pi/2) and if sin^4alpha+4cos^4beta+2=4sqrt2 sinalphacosbeta then the value of cos(alpha+beta)-cos(alpha-beta) is (A) sqrt2 (B) 1/sqrt2 (C) -1/sqrt2 (D) -sqrt2

If 2 sin 2alpha= | tan beta+ cot beta |alpha,beta, in((pi)/(2),pi) , then the value of alpha+beta is

Let alpha, beta be such that pi lt alpha-betalt3pi if sin alpha+sinbeta = -21/65 and cos alpha+cos beta = -27/65 , then the value of cos(alpha-beta)/(2) is

If g(x) is a differentiable function such that int_(1)^(sinalpha)x^(2)g(x)dx=(sin alpha-1), AA alpha in (0,(pi)/(2)) , then the value of g((1)/(3)) is equal to

If l=int_(0)^(pi//2)(cosx)/(1+sin^(2)x)dx , then (4)/(pi)l is _______.