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# Inverse Trigonometric Functions

At Saralstudy, we are providing you with the solution of Class 12th mathematics Inverse Trigonometric Functions according to the latest NCERT (CBSE) Book guidelines prepared by expert teachers. Here we are trying to give you a detailed answer to the questions of the entire topic of this chapter so that you can get more marks in your examinations by preparing the answers based on this lesson. We are trying our best to give you detailed answers to all the questions of all the topics of Class 12th mathematics Inverse Trigonometric Functions so that you can prepare for the exam according to your own pace and your speed.

In the previous chapter, types of functions are mentioned. If the function is not one-one, onto or both, then its inverse does not exist. This is the primary condition for inverse which must be fulfilled. Knowledge of the domain of range which we acquired earlier would help us in this chapter for graphing of inverse trigonometric functions. Trigonometric functions which are not one-one, onto or both will not be discussed. It has wide applications in engineering and other science related branches. This chapter consists of range, domain and principle value branches, graphs, elementary properties.

Download pdf of NCERT Solutions for Class mathematics Chapter 2 Inverse Trigonometric Functions

Download pdf of NCERT Examplar with Solutions for Class mathematics Chapter 2 Inverse Trigonometric Functions ### Exercise 1

•  Q1 Find the principal value of \begin{align} sin^{-1}\left(-\frac{1}{2}\right)\end{align} Q2 Find the principal value of \begin{align} cos^{-1}\left(\frac{\sqrt3}{2}\right)\end{align} Q3 Find the principal value of \begin{align} cosec^{-1}\left({2}\right)\end{align} Q4 Find the principal value of \begin{align} tan^{-1}\left(-\sqrt3\right)\end{align} Q5 Find the principal value of \begin{align} cos^{-1}\left(-\frac{1}{2}\right)\end{align} Q6 Find the principal value of \begin{align} tan^{-1}\left(-1\right)\end{align} Q7 Find the principal value of \begin{align} sec^{-1}\left(\frac{2}{\sqrt3}\right)\end{align} Q8 Find the principal value of \begin{align} cot^{-1}\left(\sqrt3\right)\end{align} Q9 Find the principal value of \begin{align} cos^{-1}\left(-\frac{1}{\sqrt2}\right)\end{align} Q10 Find the principal value of \begin{align} cosec^{-1}\left({-\sqrt2}\right)\end{align} Q11 Find the principal value of \begin{align} tan^{-1} (1) + cos^{-1}\left(-\frac{1}{2}\right) + sin^{-1}\left(-\frac{1}{2}\right)\end{align} Q12 Find the principal value of \begin{align} cos^{-1}\left(\frac{1}{2}\right) + 2sin^{-1}\left(\frac{1}{2}\right)\end{align} Q13 Find the value of if \begin{align} sin^{-1} x= y,\end{align} then \begin{align} (A) 0 ≤ y ≤ x \;\;\;\;\; (B) -\frac{\pi}{2} ≤ y ≤ \frac{\pi}{2} \end{align} \begin{align} (C)\; 0 < y < \pi \;\;\;\;\; (D) -\frac{\pi}{2} < y < \frac{\pi}{2} \end{align} Q14 Find the value of if \begin{align} tan^{-1}\sqrt3 - sec^{-1}(-2)\end{align} is equal to \begin{align} (A) \pi \;\;(B) -\frac{\pi}{3}\;\; (C) \frac{\pi}{3} \;\;(D) \frac{2\pi}{3}\end{align}

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