Question

$Therangeofsi{n}^{-1}x-co{s}^{-1}xis$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$si{n}^{-1}x-co{s}^{-1}x=\frac{\pi }{2}-co{s}^{-1}x-co{s}^{-1}x=\frac{\pi }{2}-2co{s}^{-1}x0\le co{s}^{-1}x\le \pi \Rightarrow 0\le 2co{s}^{-1}x\le 2\pi \Rightarrow -2\pi \le -2co{s}^{-1}x\le 0\Rightarrow \frac{-3\pi }{2}\le \frac{\pi }{2}-2co{s}^{-1}x\le \frac{\pi }{2}\therefore Range=[\frac{-3\pi }{2},\frac{\pi }{2}]$