Which of the following is the principal value branch of $c o s^{- 1} x ?$

(a) $[- \frac{π}{2}, \frac{π}{2}]$ (b) $(0, π)$ (c) $[0, π]$ (d) $(0, π) - {\frac{π}{2}}$

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Solution

(c) We know that, the principal value branch of $c o s^{- 1} x i s [0, π] .$

$∴ y = c o s^{- 1} x$

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Which of the following is the principal value branch of $c o s e c^{- 1} x ?$

(a) $(\frac{- π}{2}, \frac{π}{2})$ (b) $[0, π] - {\frac{π}{2}}$ (c) $[\frac{π}{2}, \frac{π}{2}]$ (d) $[\frac{- π}{2}, \frac{π}{2}] - [0]$

f (x) = c o s x, 0 \leq x \leq \frac{π}{2}

(2 - i) (1 - 2 i)^{2}

a + \frac{π}{2} < 2 {tan}^{- 1} x + 3 {cot}^{- 1} x < b

^{'} a^{'}

^{'} b^{'}

f (x) = [s i n x], 0 < x < 2 π

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