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Find the values of the following:

11. \(tan^{-1}(1)\)+\(cos^{-1}({-\frac{1}{\sqrt 2}})\)+\(sin^{-1}({-\frac{1}{\sqrt 2}})\).

Inverse Trigonometric Functions

Exercise 2.1

Ncert solutions class 12 chapter 2 Inverse Trigonometric Functions exercise 1
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Class 12

Inverse Trigonometric Functions

Exercise 2.1

Find the principal values of the following:

1. \(sin^{-1}({-\frac{1}{2}})\)

2. \(cos^{-1}({\frac{\sqrt{3}}{2}})\)

3. \(cosec^{-1}(2)\)

4. \(tan^{-1}(-\sqrt{3})\)

5. \(cos^{-1}({-\frac{1}{2}})\)

6. \(tan^{-1}(-1)\)

7. \(sec^{-1}({\frac{2}{\sqrt 3}})\)

8. \(cot^{-1}(\sqrt 3)\)

9. \(cos^{-1}({-\frac{1}{\sqrt 2}})\)

10. \(cosec^{-1}(-\sqrt{2})\)

Find the values of the following:

11. \(tan^{-1}(1)\)+\(cos^{-1}({-\frac{1}{\sqrt 2}})\)+\(sin^{-1}({-\frac{1}{\sqrt 2}})\).

12. \(cos^{-1}({\frac{1}{\sqrt 2}})\)+2\(sin^{-1}({\frac{1}{\sqrt 2}})\).

13. If \(sin^{-1}x=y\), then

(A) \(0\le y\le\pi\)

(B) \(-\frac{\pi}{2}\le y \le -\frac{\pi}{2}\)

(C) \(0 < y <\pi\)

(D) \(-\frac{\pi}{2} < y < -\frac{\pi}{2}\) 

14. \(tan^{-1}{\sqrt{3}}-sec^{-1}(-2)\) is equal to:

(A) \(\pi\)

(B) \(-\frac{\pi}{3}\)

(C) \(\frac{\pi}{3}\)

(D) \(\frac{2\pi}{3}\)