JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

1 of 1

Application +4 | -1

\mathrm{\theta } = {\sin ^{ - 1}}x + {\cos ^{ - 1}}x - {\tan ^{ - 1}}x,\;1 \le x < \infty

, then the smallest interval in which

\mathrm{\theta }

lies is

View answer and explanation

Correct option: B

0 \le \mathrm{\theta } \le \frac{\pi }{4}

Option D (

\frac{\pi }{4} \le \mathrm{\theta } \le \frac{\pi }{2}

) is incorrect. Option B (

0 \le \mathrm{\theta } \le \frac{\pi }{4}

) is correct because by simplifying the expression and using the given range of

x

, the smallest interval in which

\theta

lies is

[0, \frac{\pi}{4}]

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