Question

Calculate (192 - 214)
sin ((1/2) arc(cos) (7/32)).

Answer 1

$\sin \left(\frac{1}{2}\right){\cos }^{-1}\left(\frac{7}{32}\right)$

Let $=x$

$\frac{1}{2}{\cos }^{-1}\frac{7}{32}={\sin }^{-1}x$

${\cos }^{-1}\frac{7}{32}=2{\sin }^{-1}x$

${\cos }^{-1}\frac{7}{32}={\sin }^{-1}\left(2x\sqrt{1-x^2}\right)$

${\cos }^{-1}\frac{7}{32}=$