First slide

Introduction to ITF

Question

For the equation $\cos^{- 1} x + \cos^{- 1} 2 x + π = 0$ , the number of real solutions is

Moderate

A

1
B

2
C

0
D

$\infty$

Solution

we have $\cos^{- 1} x + \cos^{- 1} (2 x) = - π$ , which is not possible as $\cos^{- 1} x$ and $\cos^{- 1} 2 x$ never take negative values. $(∵ \cos^{- 1} x, \cos^{- 1} 2 x \in [0, π])$

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