HOTS Questions Inverse Trigonometry Lecture 4 Part 3

Advertisements

Part - 3 Lecture - 4 Chapter 2 Inverse Trigonometric Functions

“I find that when you have a real interest in life and a curious life, that sleep is not the most important thing.” –Martha Stewart

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

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)

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 \(\sin y=\tan ^{2} \frac{x}{2} \)

Advertisements