Question

If ${\sin }^{-1}1+{\sin }^{-1}\frac{4}{5}={\sin }^{-1}x$ , the what is x equal to ?

• A. 3/5
• B. 4/5
• C. 1
• D. 0

Answer 1

The correct option is A 3/5

We know that,

${\sin }^{-1}a+{\sin }^{-1}b={\sin }^{-1}(a\sqrt{1-(b{)}^2}+b\sqrt{1-(a{)}^2})$

Then,

${\sin }^{-1}1+{\sin }^{-1}0.8={\sin }^{-1}x$

$\Rightarrow {\sin }^{-1}(1\sqrt{1-(0.8{)}^2}+0.8\sqrt{1-(1{)}^2})={\sin }^{-1}x$

$\Rightarrow {\sin }^{-1}\left(0.6\right)={\sin }^{-1}x$

$\Rightarrow x=0.6=\frac{3}{5}$

Hence, A is correct.