Question

What is the value of $\cos \left(2{\cos }^{-1}0.8\right)$?

• A. $0.81$
• B. $0.56$
• C. $0.48$
• D. $0.28$

Answer 1

The correct option is D $0.28$

Let $2{\cos }^{-1}0.8=\theta$

$\therefore {\cos }^{-1}0.8=\frac{\theta }{2}$

$\therefore \cos \left(\frac{\theta }{2}\right)=0.8$

We know,

$1+\cos \theta =2{\cos }^2\left(\frac{\theta }{2}\right)$

$\therefore 1+\cos \theta =2(0.8{)}^2$

$\therefore 1+\cos \theta =1.28$

$\therefore \cos \theta =0.28$

$\therefore \theta ={\cos }^{-1}\left(0.28\right)$

$\Rightarrow \cos \left(2{\cos }^{-1}0.8\right)$

$=\cos \left(\theta \right)$

$=\cos \left({\cos }^{-1}\right(0.28\left)\right)$

$=0.28$

So, the answer is $0.28$.