Question

$\cos [2{\sin }^{-1}\frac{3}{4}+{\cos }^{-1}\frac{3}{4}]=$

• A. $\frac{3}{5}$
• B. $\frac{-3}{4}$
• C. does not exist
• D. $\frac{3}{4}$

Answer 1

The correct option is B $\frac{-3}{4}$

$\cos [{\sin }^{-1}\frac{3}{4}+{\sin }^{-1}\frac{3}{4}+{\cos }^{-1}\frac{3}{4}]$$=\cos [\frac{\pi }{2}+{\sin }^{-1}\frac{3}{4}]=-\sin \left({\sin }^{-1}\frac{3}{4}\right)=-\frac{3}{4}$