The correct option is C f(x)=π x,π/2≤ x≤π sin^ 1(sin(x)) =π x #160; #160;if x lies in the second or third quadrant.That is π2≤ ...

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Solving Simultaneous Trigonometric Equations

If fx=sin-1...

Question

If $f (x) = {sin}^{- 1} (sin x)$

f (x) = π - x, 0 \leq x \leq \frac{π}{2}

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f (x) = π - x, \frac{π}{2} \leq x \leq π

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f (x) = x, 0 \leq x \leq π

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f (x) = - x, \frac{π}{2} \leq x \leq 0

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Solution

The correct option is C $f (x) = π - x, \frac{π}{2} \leq x \leq π$
${sin}^{- 1} (sin (x))$ $= π - x$ if $x$ lies in the second or third quadrant.

That is
$\frac{π}{2} \leq x \leq π$ or $\frac{π}{2} \leq x \leq \frac{3 π}{2}$

Hence, option 'B' is correct.

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