Evaluate the expression? sin(cos^(-1)(3/4)-sin^(-1)(1/2))

1 Answer
May 8, 2018

(sqrt21-3)/8.

Explanation:

Suppose that, cos^-1(3/4)=theta in [0,pi]. :. costheta=3/4......(1).

:. sintheta=sqrt(1-cos^theta)=sqrt(1-9/16)=+-sqrt7/4.

But, costheta=3/4 gt 0, theta in [0,pi] rArr theta in Q_1=[0,pi/2].

:. sintheta=+sqrt7/4............(2).

We know that, sin^-1(1/2)=pi/6.

:." The Exp."=sin(theta-pi/6),

=sinthetacos(pi/6)-costhetasin(pi/6),

=sqrt7/4*sqrt3/2-3/4*1/2,

=(sqrt21-3)/8.