Assertion :The number of solutions of the equation $cos x = a^{x} + a^{- x}$ is zero. Reason: Because $- 1 \leq cos x \leq 1$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion false but Reason is true

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$a^{x} + a^{- x} \geq 2 a n d | cos x | \leq 1$
$∴ a^{x} + a^{- x} = cos x$ having so solution
Hence, assertion is correct.
Also, $- 1 \leq cos \leq 1$
$| cos x | \leq 1$
Hence, reason is correct and is the correct explanation for assertion

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