If - 2 - x- 3- 2- then sin -1 sin x is equal to

The correct option is D π x We have, π #160; 2 ≤ x≤ 3π #160; 2 ⇒ π #160; 2 ≤ x π≤π #160; 2 ⇒ π #160; 2 ≤π x≤π #160; 2 ...

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Antiderivative

If π 2 ≤ x≤...

Question

If $\frac{π}{2} \leq x \leq \frac{3 π}{2}$ , then ${sin}^{- 1} (sin x)$ is equal to

x

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- x

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π + x

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π - x

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Solution

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sin (x) = - \frac{1}{3}

π \leq x \leq 3 \frac{π}{2}

cot (2 x) =

\frac{π}{2} < x < \frac{3 π}{2}

\sqrt{\frac{1 - sin x}{1 + sin x}}

x \in (π, \frac{3 π}{2})

\sqrt{\frac{1 - sin x}{1 + sin x}}

1 + sin x + {sin}^{2} x + \dots \dots \infty = 4 + 2 \sqrt{3}, 0 < x < π

x \neq \frac{π}{2},

f (x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - sin x}{(π - 2 x)^{2}} \cdot \frac{log sin x}{log (1 + π^{2} - 4 π x + 4 x^{2})}, & x \neq \frac{π}{2} k, & x = \frac{π}{2} \end{matrix}

x = \frac{π}{2}

k

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