CBSE Class 12 Maths

Inverse Trigonometric Functions

Each concept is a short lesson, then questions until you get three right.

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4 concepts, a short lesson each

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Principal values of inverse functions

$\sin^{-1}$ in $[-\frac{\pi}{2}, \frac{\pi}{2}]$ , $\cos^{-1}$ in $[0, \pi]$ , $\tan^{-1}$ in $(-\frac{\pi}{2}, \frac{\pi}{2})$ : one angle, in that range

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Principal values of inverse functions $\sin^{-1}$ in $[-\frac{\pi}{2}, \frac{\pi}{2}]$ , $\cos^{-1}$ in $[0, \pi]$ , $\tan^{-1}$ in $(-\frac{\pi}{2}, \frac{\pi}{2})$ : one angle, in that rangeStart
sin⁻¹(sin x) and its relatives $\sin^{-1}(\sin x) = x$ only for $x$ in the principal range; otherwise find the angle in the range with the same sineStart
Properties of inverse functions $\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}$ ; $\tan^{-1}x + \tan^{-1}y = \tan^{-1}\dfrac{x + y}{1 - xy}$ when $xy < 1$ Start
Equations in inverse functionsCombine the inverse terms with the properties, take the ratio of both sides, then keep only roots in the principal rangesStart

Practise Inverse Trigonometric Functions

Once the concepts click, try the questions your exam asks.

Textbook exercisesEvery exercise, with model answers Past board questionsAsked from this chapter, with solutions

Inverse trigonometric functions0 of 4

Practise Inverse Trigonometric Functions