40. Prove that cos x + sec x is not equal to 3/2 for all real x.

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2^{sin x} + 2^{cos x} \leq 2^{1 - \frac{1}{\sqrt{2}}}

x

\sec (x + α) + \sec (x - α) = 2 \sec x

\cos x = \pm \sqrt{2} \cos \frac{α}{2}

|\cos x \cos (\frac{π}{3} - x) \cos (\frac{π}{3} + x)| \leq \frac{1}{4}

[sin x + sec x]^{2} + [cos x + csc x]^{2} = [1 + sec x . csc x]^{2}

s e c^{2} x + c o s^{2} x \geq 2

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