if-2-sin-x-2-cos-x-2-1-1-2-then-find-the-value-of-x-

Question Number 90507 by student work last updated on 24/Apr/20

if 2^{\sin x} + 2^{\cos x} = 2^{1 + \frac{1}{\sqrt{2}}} then find the value of x = ?

Commented by student work last updated on 24/Apr/20

who can solve ?

Commented by MJS last updated on 24/Apr/20

x = \frac{π}{4} + 2 n π; n \in Z

\sin \frac{π}{4} = \cos \frac{π}{4} = \frac{\sqrt{2}}{2}

2^{\frac{\sqrt{2}}{2}} + 2^{\frac{\sqrt{2}}{2}} = 2 \times 2^{\frac{\sqrt{2}}{2}} = 2^{1 + \frac{\sqrt{2}}{2}} = 2^{1 + \frac{1}{\sqrt{2}}}

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