sin(\left( \frac{1}{2}\cos^{- 1}\frac{4}{5} \right))= | MATH - PRINCIPAL & GENERAL VALUE OF I.T.F | SolveeIt

sin $\left( \frac{1}{2}\cos^{- 1}\frac{4}{5} \right)$ =

$\frac{1}{\sqrt{10}}$

– 10

$\frac{1}{10}$

– $\frac{1}{10}$

Answer

$\frac{1}{\sqrt{10}}$

Explanation

Let cos^–1 4/5 = x ̃ cos x = 4/5 …(i)

Now sin ( $\frac{1}{2}\cos^{- 1}\frac{4}{5}$ ) = sin (x/2) …(ii)

From (i) cos x = $\frac{4}{5}$

̃ 1–2 sin²x/2 = $\frac{4}{5}$

̃ sin x/2 = $1/\sqrt{10}$

Question: sin\(\left( \frac{1}{2}\cos^{- 1}\frac{4}{5} \right)\)=...