" 12."lt(sin(x-(pi)/(6)))/(x rarr(pi)/(6))()/(sqrt(3)-2cos x)

lim_ (x rarr (pi) / (6)) (sin (x- (pi) / (6))) / (sqrt (3) -cos x)

lim_(theta rarr(pi)/(6))((sin(theta-(pi)/(6)))/(sqrt(3)-2cos theta)

Evaluate: lim_(h rarr0)(2[sqrt(3)sin((pi)/(6)+h)-cos((pi)/(6)+h)])/(sqrt(3)h(sqrt(3)cos h-sin h))

(i) lim_(x to (pi)/(2)) (1+cos 2x)/((pi-2x)^(2)) (ii) lim_( x to 0) (1-cos x.sqrt(cos 2x))/(x^(2)) (iii) lim_(thetararr(pi)/(6)) (sin(theta-(pi)/(6)))/(sqrt(3)-2 cos theta)

lim_ (x rarr (pi) / (6)) (3sin x-sqrt (3) cos x) / (6x-pi)

lim_(h rarr 0) ([2 sqrt(3) sin ((pi)/(6) + h) - cos ((pi)/(6) + h)])/(sqrt(3) h (sqrt(3) cos h - sin h)) is :

" sin " (x-(pi)/(6)) + " cos " (x-(pi)/(3)) =sqrt(3) " sin " x

Evaluate the following limits : Lim_( x to pi//6) (sin (x - pi/6))/(sqrt(3)/2 - cos x )

Evaluate the definite integrals int_((pi)/(6))^((pi)/(3))(sin x+cos x)/(sqrt(sin2x))dx