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What is the value of $\cos \left(2 \cos ^{-1}(0.8) ?\right.$
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Verified Answer
The correct answer is:
$0.28$
We know that
$2 \cos ^{-1} x=\cos ^{-1}\left(2 x^{2}-1\right)$
here, $x=0.8$
$\therefore \quad 2 \cos ^{-1}(0.8)=\cos ^{-1}\left(2(0.8)^{2}-1\right)$
$=\cos ^{-1}(0.28)$
Now, $\cos \left(\cos ^{-1}(x)\right)=x$
$\therefore \cos \left(\cos ^{-1}(0.28)\right)=0.28$
$2 \cos ^{-1} x=\cos ^{-1}\left(2 x^{2}-1\right)$
here, $x=0.8$
$\therefore \quad 2 \cos ^{-1}(0.8)=\cos ^{-1}\left(2(0.8)^{2}-1\right)$
$=\cos ^{-1}(0.28)$
Now, $\cos \left(\cos ^{-1}(x)\right)=x$
$\therefore \cos \left(\cos ^{-1}(0.28)\right)=0.28$
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