Inverse Trigonometric Functions Lecture 5 Part 2

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Part - 2 Lecture - 5 Chapter 2 Inverse Trigonometric Functions

“Too many of us are not living our dreams because we are living our fears. ” –Les Brown

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

Questions discussed in this lecture

Solve:
9. \(\tan ^{-1} (x-1)+\tan ^{-1} x+\tan ^{-1} (x+1)=\tan ^{-1} 3x\)

10. \(3\sin ^{-1} \frac{2x}{1+x^{2} } -4\cos ^{-1} \frac{1-x^{2} }{1+x^{2} } +2\tan ^{-1} \frac{2x}{1-x^{2} } =\frac{\pi }{3} \)

11. If \(\sin ^{-1} \frac{2a}{1+a^{2} } -\cos ^{-1} \frac{1-b^{2} }{1+b^{2} } =\tan ^{-1} \frac{2x}{1-x^{2} } \), then prove that \( x=\frac{a-b}{1+ab}.\)

12. Evaluate: \(\tan ^{-1} \left(\frac{a+bx}{b-ax} \right), x<\frac{b}{a} \)

13. Prove: \( \tan ^{-1} \left(\frac{a-b}{1+ab} \right)+\tan ^{-1} \left(\frac{b-c}{1+bc} \right)+\tan ^{-1} \left(\frac{c-a}{1+ca} \right)=0\)

14. If \(\tan ^{-1} x+\tan ^{-1} y=\frac{4\pi }{5} \), then find the value of \(\cot ^{-1} x+\cot ^{-1}y\)?

15. If \(\tan ^{-1} \left(\frac{1}{1+1.2} \right)+\tan ^{-1} \left(\frac{1}{1+2.3} \right)+…+\tan ^{-1} \left(\frac{1}{1+n.(n+1)} \right)=\tan ^{-1} \phi \), then find the value of \(\phi\).

16. If \((\tan ^{-1} x)^{2} +(\cot ^{-1} x)^{2} =\frac{5\pi ^{2} }{8} \), then find x.

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