##### Question 1:

Find the principal values of the following

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##### Question 2:

Find the principal values of the following

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##### Question 3:

Find the principal values of the following
cosec^{–1}(2)

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##### Question 4:

Find the principal values of the following

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##### Question 5:

Find the principal values of the following

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##### Question 6:

Find the principal values of the following
tan^{–1–1}(– 1)

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##### Question 7:

Find the principal values of the following

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##### Question 8:

Find the principal values of the following

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##### Question 9:

Find the principal values of the following

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##### Question 10:

Find the principal values of the following

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##### Question 11:

Find the value of the following

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##### Question 12:

Find the value of the following

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##### Question 13:

If sin^{–1} x = y, then :

- 0$\le $ y$\le $ $\mathrm{\pi}$
- 0 < y < $\mathrm{\pi}$

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##### Question 14:

- $\mathrm{\pi}$

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##### Question 15:

Prove the following

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Let sin^{−1} x = $\mathrm{\theta}$ so that x = sin $\mathrm{\theta}$.

##### Question 16:

Prove the following

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Let cos^{−1} x = $\mathrm{\theta}$ so that x = cos $\mathrm{\theta}$.

##### Question 17:

Prove the following

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##### Question 18:

Prove the following

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##### Question 19:

Write the following functions in the simplest form :

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##### Question 20:

Write the following functions in the simplest form :

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##### Question 21:

Write the following functions in the simplest form :

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##### Question 22:

Write the following functions in the simplest form :

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##### Question 23:

Write the following functions in the simplest form :

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##### Question 24:

Write the following functions in the simplest form :

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##### Question 25:

Find the value of each of the following

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##### Question 26:

Find the value of each of the following

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##### Question 27:

Find the value of each of the following

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##### Question 28:

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##### Question 29:

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##### Question 30:

Find the value of each of the expressions

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##### Question 31:

Find the value of each of the expressions

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##### Question 32:

Find the value of each of the expressions

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##### Question 33:

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##### Question 34:

- 1

##### Answer:

1

##### Question 35:

- $\mathrm{\pi}$
- 0

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##### Question 36:

If sin^{–1} x = y, then :

- 0$\le $ y$\le $ $\mathrm{\pi}$
- 0 < y < $\mathrm{\pi}$

##### Answer:

##### Question 37:

- $\mathrm{\pi}$

##### Answer:

##### Question 38:

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##### Question 39:

- 1

##### Answer:

1

##### Question 40:

- $\mathrm{\pi}$
- 0

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##### Question 41:

sin (tan^{–1} x), | x | < 1, is equal to :

##### Answer:

##### Question 42:

- 0

##### Answer:

0