Q196 / 270 · NDA 2016 (Phase 2) · Mathematics
What is the value of $\cos \left(2 \cos ^{-1}(0.8)\right.$ ?
- A$0.81$
- B$0.56$
- C$0.48$
- Correct answerD$0.28$
Solution
We know that
$\begin{aligned}
& 2 \cos ^{-1} x=\cos ^{-1} x\left(2 x^2-1\right) \\
& \text { here } x=0.8 \\
& \begin{aligned}
\therefore \quad 2 \cos ^{-1}(0.8) & =\cos ^{-1}\left(2(0.8)^2-1\right) \\
& =\cos ^{-1}(0.28)
\end{aligned}
\end{aligned}$
Now, $\left(\cos ^{-1}(x)\right)=x$.
$\therefore \cos \left(\cos ^{-1}(0.28)\right)=0.28$
Hence, the correct answer is option: 'D'.