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

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Answer 1 · 2018-05-08T18:08:46

# (sqrt21-3)/8#.

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#.