s i n − 1 | c o s x | − c o s − 1 | s i n x | = a has at least one solution if a ∈ Options: A . &nbsp 0 B . &nbsp [ 0 , π 2 ] C . &nbsp [ π 2 , 3 π 2 ] D . &nbsp ( 0 , π )

sin−1|cosx|−cos−1|sinx|=a has at least one solution if a

Question -

$s i n^{- 1} | c o s x | - c o s^{- 1} | s i n x | = a$ has at least one solution if a $\in$

Options:

A .

0

B .

[0, \frac{π}{2}]

C .

[\frac{π}{2}, \frac{3 π}{2}]

D .

(0, π)

Answer: Option A
:
A

s i n^{- 1} | c o s x | - c o s^{- 1} | s i n x | = \frac{π}{2} - c o s^{- 1} | c o s x | - \frac{π}{2} + s i n^{- 1} | s i n x | = a \Rightarrow s i n^{- 1} | s i n x | - c o s^{- 1} | c o s x | = a \Rightarrow a = 0 \forall x

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