If 0≤x≤1, then cos−1⁡2x2−1 equals - Infinity Learn by Sri Chaitanya

A
$2 \cos^{- 1} x$
B
$π - 2 \cos^{- 1} x$
C
$2 π - 2 \cos^{- 1} x$
D
none of these

Solution:

Let $\cos^{- 1} x = θ .$ Then, $x = \cos θ$

Also, $0 \leq x \leq 1 \Rightarrow 0 \leq \cos θ \leq 1 \Rightarrow 0 \leq θ \leq \frac{π}{2}$

Now,

$\begin{aligned} \cos^{- 1} (2 x^{2} - 1) = \cos^{- 1} (2 \cos^{2} θ - 1) = \cos^{- 1} (\cos 2 θ) \\ = 2 θ = 2 \cos^{- 1} x [∵ 0 \leq 2 θ \leq π] \end{aligned}$

If $0 \leq x \leq 1,$ then $\cos^{- 1} (2 x^{2} - 1)$ equals

Solution:

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