inverse_trigonometric_functions_lecture_3_part_2
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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\}