How do you solve and find the value of sin(cos^-1(3/4))sin(cos−1(34))?

1 Answer
Ratnaker Mehta
Mar 2, 2017

sqrt7/4.√74.

Explanation:

Let, cos^-1(3/4)=theta.cos−1(34)=θ.

Knowing that, cos^-1 x=theta iff x=costheta, theta in [0,pi],cos−1x=θ⇔x=cosθ,θ∈[0,π], we get,

costheta=3/4, and, 0 le theta le pi.cosθ=34,and,0≤θ≤π.

But costheta >0 rArr theta !in [pi/2,pi] rArr 0 le theta le pi/2.cosθ>0⇒θ∉[π2,π]⇒0≤θ≤π2.

:. sintheta=+-sqrt(1-cos^2theta)=+-sqrt(1-9/16)=+-(sqrt7)/4.

0 le theta le pi/2 rArr sin theta gt 0 rArr sin theta=+sqrt7/4.

:. sin (cos^-1(3/4))=sintheta=sqrt7/4.

Enjoy Maths.!

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