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# Need help

I was reading a math book that says that the function below is less or equal to 3. Why is that?

$\Large 2^{\sin^2 x} + \dfrac2{2^{\sin^2 x}}$

Note by Yossi Levi
3 months, 1 week ago

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Let $$\large f(x) = 2^{\sin^2 x} + \dfrac{2}{2^{\sin^2 x}}$$

$$\large \Rightarrow 2^{\sin^2 x}+2^{\cos^2 x}$$

which has a maximum value of $$3$$, equality at $$x=\frac{\pi}{2} + n\pi$$ or $$x = n\pi$$

where $$n$$ is a whole number. · 3 months, 1 week ago