`f(x)=cos(pi/(sqrt(3))sinx+sqrt(2/3)picosx)`

lim_(x to (pi)/(6)) [(3sinx - sqrt(3)cos x)/(6x -pi)] is equal to

f(x)=x^(2)-2sqrt(sin*sqrt(3)-sin sqrt(2))x-(cos sqrt(3)-cos sqrt(2))

Evaluate int_0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cos x))dx

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

The derivative of the function, f(x)=cos^(-1){(1)/(sqrt(13))(2cosx-3sinx)}+sin^(-1){(1)/(sqrt(13))(2cosx+3sinx)}w.r.tsqrt(1+x^(2)) is

Evaluate int_(pi//6)^(pi//3) (sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx

Evaluate int_((pi)/(6))^((pi)/(3))(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx

In each of the following cases find the period of the function if it is periodic. (i) f(x)="sin"(pi x)/(sqrt(2))+"cos"(pi x)/(sqrt(3)) " (ii) " f(x)="sin"(pi x)/(sqrt(3))+"cos"(pi x)/(2sqrt(3))