`lim_(theta-gtpi/6)(sin(theta-pi/6)/(sqrt(3)-2costheta)`

(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)

Prove that sin(theta-(pi)/(6))+cos(theta-(pi)/(3))=sqrt(3)sin theta

Evaluate the following limits : Lim_(theta to pi/2) (1-sin theta)/((pi/2-theta)cos theta)

The value of the determinant |(sintheta, costheta, sin2theta) , (sin(theta+(2pi)/3), cos(theta+(2pi)/3), sin(2theta+(4pi)/3)) , (sin(theta-(2pi)/3), cos(theta-(2pi)/3), sin(2theta-(4pi)/3))|

lim_(theta rarr(pi)/(6))(4cos^(2)theta-3)/(2sin theta-1)

The value of the determinant |[sintheta, costheta, sin2theta] , [sin(theta+(2pi)/3), cos(theta+(2pi)/3), sin(2theta+(4pi)/3)] , [sin(theta-(2pi)/3), cos(theta-(2pi)/3), sin(2theta-(4pi)/3)|

lim_(theta rarr(pi)/(4))(1-tan theta)/(1-sqrt(2)sin theta)

Evaluate the limits : Lim_(theta to pi/6) (cot^(2) theta - 3)/(" cosec " theta - 2)