inverse_trigonometric_functions_lecture_4_part_3
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Questions discussed in this lecture

Prove:
21. \tan ^{-1} \frac{63}{16} =\sin ^{-1} \frac{5}{13} +\cos ^{-1} \frac{3}{5}
(NCERT Miscellaneous Exercise Q7)

22. \cos ^{-1} \frac{4}{5} +\cos ^{-1} \frac{12}{13} =\cos ^{-1} \frac{33}{65}
(NCERT Miscellaneous Exercise Q5)

23. \cos ^{-1} \frac{12}{13} +\sin ^{-1} \frac{3}{5} =\sin ^{-1} \frac{56}{65}
(NCERT Miscellaneous Exercise Q6)

24. \sin ^{-1} \frac{12}{13} +\cos ^{-1} \frac{4}{5} +\tan ^{-1} \frac{63}{16} =\pi
(NCERT Example 11)

inverse_trigonometric_functions_lecture_4_part_3
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25. 2\tan ^{-1} \left\{\tan \frac{\alpha }{2} \tan \left(\frac{\pi }{4} -\frac{\beta }{2} \right)\right\}=\tan ^{-1} \frac{\sin \alpha \cos \beta }{\cos \alpha +\sin \beta }

26. 2\tan ^{-1} \left(\sqrt{\frac{a-b}{a+b} } \tan \frac{\theta }{2} \right)=\cos ^{-1} \left(\frac{a\cos \theta +b}{a+b\cos \theta } \right)

27. If \sin \left(\sin ^{-1} \frac{1}{5} +\cos ^{-1} x\right)=1, then find the value of x.
(NCERT Exercise 2.2 Q14)

28. If y=\cot ^{-1} (\sqrt{\cos x} )-\tan ^{-1} (\sqrt{\cos x} ), prove that \sin y=\tan ^{2} \frac{x}{2}