Let S = x ∈ R : cos x + cos 2 x 2 , then

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Question: Answered & Verified by Expert

Let

S = \{x \in R : \cos (x) + \cos (\sqrt{2} x) < 2\},

then

MathematicsSets and RelationsKVPYKVPY 2018 (SB/SX)

Options:

A $S = ϕ$
B $S$ is a non-empty finite set
C $S$ is an infinite proper subset of $R - \{0\}$
D $S = R - \{0\}$

Solution:

2726 Upvotes Verified Answer

The correct answer is:

S = R - \{0\}

We have,

$S = \{x \in R : \cos x + \cos \sqrt{2} x < 2\}$

Maximum value of $\cos x$ and $\cos \sqrt{2} x$ is $1$ at $x = 0$

$∴ \cos x + \cos \sqrt{2} x = 2$ at $x = 0$

Hence, $S = R - \{0\}$

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