Question

Domain and Rariges of cos^–1 is:-

विकल्प

• ${\displaystyle [-1,1],[\frac{-\pi }{2},\frac{\pi }{2}]}$

• ${\displaystyle [-1,1],[0,\pi ]}$

• ${\displaystyle R,(\frac{-\pi }{2},\frac{\pi }{2})}$

• ${\displaystyle R,(0,\pi )}$

Answer 1

${\displaystyle [-1,1],[0,\pi ]}$

Explanation:

sin^–1 : ${\displaystyle [-1,1]\to [-\frac{\pi }{2},\frac{\pi }{2}]}$

cos^–1 : ${\displaystyle [-1,1]\to [0,\pi ]}$

cosec^–1 : ${\displaystyle R-(-1,1)\to [-\frac{\pi }{2},\frac{\pi }{2}]-\left|0\right|}$

sec^–1 : ${\displaystyle R-(-1,1)\to [0,\pi ]-\left|\frac{\pi }{2}\right|}$

tan^–1 : ${\displaystyle R\to (-\frac{\pi }{2},\frac{\pi }{2})}$

cot^–1 : ${\displaystyle R-(0,\pi )}$