## INVERSE TRIGONOMETRIC FUNCTIONS CLASS 12 IMPORTANT QUESTIONS

### Inverse Trigonometric Functions Class 12 Important Questions PDF

1. Evaluate the following :

2. Express in the simplest form:

3. Prove that :

4.Prove that :
${\mathrm{tan}}^{-1}\left\{\frac{\sqrt{1+{x}^{2}}+\sqrt{1-{x}^{2}}}{\sqrt{1+{x}^{2}}-\sqrt{1-{x}^{2}}}\right\}=\frac{\pi }{4}+\frac{1}{2}{\mathrm{cos}}^{-1}{x}^{2},-1

5. Simplify each of the following :

6. Simplify each of the following :

7. Evaluate :

8. Prove that :

9. Find the value of
$\mathrm{cot}\left({\mathrm{tan}}^{-1}a+{\mathrm{cot}}^{-1}a\right)$

10. If

11. If

12. If

13. Solve : $\mathrm{sin}\left\{{\mathrm{sin}}^{-1}\frac{1}{5}+{\mathrm{cos}}^{-1}x\right\}=1$

14. Prove that : ${\mathrm{tan}}^{-1}1+{\mathrm{tan}}^{-1}2+{\mathrm{tan}}^{-1}3=\pi$

15.Prove that : ${\mathrm{sin}}^{-1}\frac{12}{13}+{\mathrm{cos}}^{-1}\frac{4}{5}+{\mathrm{tan}}^{-1}\frac{63}{16}=\pi$ ${\mathrm{sin}}^{-1}\frac{12}{13}+{\mathrm{cos}}^{-1}\frac{4}{5}+{\mathrm{tan}}^{-1}\frac{63}{16}=\pi$

16. Prove that : ${\mathrm{tan}}^{-1}\frac{1}{2}+{\mathrm{tan}}^{-1}\frac{1}{5}+{\mathrm{tan}}^{-1}\frac{1}{8}=\frac{\pi }{4}$

17. Prove that : ${\mathrm{tan}}^{-1}\frac{1}{5}+{\mathrm{tan}}^{-1}\frac{1}{7}+{\mathrm{tan}}^{-1}\frac{1}{3}+{\mathrm{tan}}^{-1}\frac{1}{8}=\frac{\pi }{4}$
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