Solveeit Logo
Login

Question

Question: In its domain, f(x) = \(\frac{\sin^{–1}x}{\cot^{–1}x}\) is –...

In its domain, f(x) = sin⁡–1xcot⁡–1x\frac{\sin^{–1}x}{\cot^{–1}x} is –

A

A increasing function

B

A strictly increasing function

C

A decreasing function

D

A strictly decreasing function

Answer

A strictly increasing function

Explanation

Solution

f '(x) = 11–x2×(cos⁡–1x–sin⁡–1x)×(–11–x2)(cos⁡–1x)2\frac{\frac{1}{\sqrt{1–x^{2}}} \times (\cos^{–1}x–\sin^{–1}x) \times \left( –\frac{1}{\sqrt{1–x^{2}}} \right)}{(\cos^{–1}x)^{2}}

= cos⁡–1x+sin⁡–1x1–x2(cos⁡–1x)2\frac{\cos^{–1}x + \sin^{–1}x}{\sqrt{1–x^{2}}(\cos^{–1}x)^{2}} = π1–x2(cos⁡–1x)2\frac{\pi}{\sqrt{1–x^{2}}(\cos^{–1}x)^{2}} = + ve

= f '(x) > 0 st. Inc. function