inverse_trigonometric_functions_lecture_3_part_3
Play Video

Questions discussed in this lecture

Simplify:
15. \tan ^{-1} \sqrt{\frac{a-x}{a+x} }

16. \tan ^{-1} \left(\frac{\cos x}{1-\sin x} \right),\, \, -\frac{\pi }{2} <x<\frac{\pi }{2} (NCERT Example 5)

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

18. \tan ^{-1} (x+\sqrt{1+x^{2} } )

19. \sin \left\{2\tan ^{-1} \sqrt{\frac{1-x}{1+x} } \right\}

20. \sin ^{-1} \left(\frac{\sin x+\cos x}{\sqrt{2} } \right)

21. \tan ^{-1} \left[\frac{a\cos x-b\sin x}{b\cos x+a\sin x} \right],\, {\rm if}\, \, \frac{a}{b} \tan x>-1 (NCERT Example 12)

22. \cot ^{-1} \left(\frac{\sqrt{1+\sin x} +\sqrt{1-\sin x} }{\sqrt{1+\sin x} -\sqrt{1-\sin x} } \right)=\frac{x}{2} ,\, \, x\in \left(0,\, \, \frac{\pi }{4} \right) (NCERT Miscellaneous Exercise Q10)

23. \tan ^{-1} \left(\frac{\sqrt{1+x} -\sqrt{1-x} }{\sqrt{1+x} +\sqrt{1-x} } \right)=\frac{\pi }{4} -\frac{1}{2} \cos ^{-1} x,\, \, -\frac{1}{\sqrt{2} } \le x\le 1 (NCERT Miscellaneous Exercise Q11)