First slide

Functions (XII)

Question

The domain of the function
f(x) = Cos^-1(sec (cos^-1X)) + sin^-1 (Cosec(sin^-1 X)) is

Moderate

A

$x \in R$
B

X= 1 , -1
C

-1 $\leq$ x $\leq$ 1
D

$x \in ϕ$

Solution

$f (x) = \cos^{- 1} (\sec (\cos^{- 1} x) + \sin^{- 1} (coses (\sin^{- 1} x)) \Rightarrow - 1 \leq \sec (\cos^{- 1} x) \leq 1 and - 1 \leq cosec (\sin^{- 1} x) \leq 1 \Rightarrow \sec (\cos^{- 1} x) = \pm 1 and cosec (\sin^{- 1} x) = \pm 1 \Rightarrow \cos^{- 1} x = 0, π and \sin^{- 1} x = \frac{π}{2}, - \frac{π}{2} \Rightarrow x = \pm 1 and x = \pm 1 ∴ Domain is x = \pm 1$

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