Question

The value of $sin\left[2co{s}^{-1}\frac{\sqrt{5}}{3}\right]$ is

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is C

We have,
$sin\left[2co{s}^{-1}\frac{\sqrt{5}}{3}\right]$
$=2sin\left(co{s}^{-1}\frac{\sqrt{5}}{3}\right)cos\left(co{s}^{-1}\frac{\sqrt{5}}{3}\right)$
$=2\sqrt{1-\frac{5}{9}},\frac{\sqrt{5}}{3}$
$=\frac{4\sqrt{5}}{9}$