# Part - 2 Lecture - 3 Chapter 2 Inverse Trigonometric Functions

“Only put off until tomorrow what you are willing to die having left undone.” –Pablo Picasso

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

Questions discussed in this \lecture

Simplify:
6. $$\tan ^{-1} \frac{x}{\sqrt{a^{2} -x^{2} } }, |x|<a$$ (NCERT Exercise 2.2 Q9)

7. $$\tan ^{-1} \left(\frac{3a^{2} x-x^{3} }{a^{3} -3ax^{2} } \right), a>0; \frac{-a}{\sqrt{3} } \le x\le \frac{a}{\sqrt{3} }$$ (NCERT Exercise 2.2 Q10)

8. $$\tan ^{-1} \left(\frac{\cos x}{1+\sin x} \right)$$

9. $$\tan ^{-1} \left(\frac{\sin x}{1+\cos x} \right)$$

10. $$\tan ^{-1} \left(\frac{a\cos x-b\sin x}{b\cos x+a\sin x} \right)$$

11. $$\tan ^{-1} \left(\frac{x}{a+\sqrt{a^{2} -x^{2} } } \right)$$

12. $$\sin ^{-1} \left(\frac{5}{13} \cos x+\frac{12}{13} \sin x\right)$$

13. $$\sin ^{-1} (x\sqrt{1-x} -\sqrt{x} \sqrt{1-x^{2} } )$$

14. $$\sin ^{-1} \left \{ \frac{\sqrt{1+x} +\sqrt{1-x} }{2} \right \}$$