The-general-solution-of-2-sin-x-2-cos-x-2-1-1-2-is-

Question Number 18472 by Tinkutara last updated on 22/Jul/17

The general solution of 2^{\sin x} + 2^{\cos x}

= 2^{1 - \frac{1}{\sqrt{2}}} is

Answered by sushmitak last updated on 22/Jul/17

\sin x \cos x = \frac{1}{2} \sin 2 x = \frac{1}{2}

2 x = 2 n π + \frac{π}{2} \Rightarrow x = 2 n π + \frac{π}{4}

Commented by sushmitak last updated on 23/Jul/17

2^{1 / \sqrt{2}} + 2^{1 / \sqrt{2}} = 2 \cdot 2^{1 / \sqrt{2}} = 2^{1 + 1 / \sqrt{2}}

answer is correct

Commented by Tinkutara last updated on 23/Jul/17

But it is 2^{1 - \frac{1}{\sqrt{2}}} .