Inverse Trigonometric Functions Lecture 5 Part 2

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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