The minimum value of x which satisfies the inequality s i n - 1 x 2 ≥ c o s - 1 x 2 is

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Question: Answered & Verified by Expert

The minimum value of

x

which satisfies the inequality

{(s i n^{- 1} x)}^{2} \geq {(c o s^{- 1} x)}^{2}

is

MathematicsInverse Trigonometric FunctionsJEE Main

Options:

A $\frac{1}{\sqrt{2}}$
B $\frac{1}{2}$
C $\frac{\sqrt{3}}{2}$
D $\frac{1}{\sqrt{3}}$

Solution:

2930 Upvotes Verified Answer

The correct answer is:

\frac{1}{\sqrt{2}}

{(s i n^{- 1} x)}^{2} - {(c o s^{- 1} x)}^{2} \geq 0

(s i n^{- 1} x + c o s^{- 1} x) (s i n^{- 1} x - c o s^{- 1} x) \geq 0

\Rightarrow s i n^{- 1} x \geq c o s^{- 1} x

Clearly from graph

x \in [\frac{1}{\sqrt{2}}, 1]

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