Question

Докажите тождество
sinx+cosx=√2cos(π/4-x)

Answer 1

$sinx+cosx=\sqrt{2}cos(\frac{\pi}{4}-x)$
$sinx+cosx=\sqrt{2}(cos\frac{\pi}{4}cosx+sin\frac{\pi}{4}sinx)$
$sinx+cosx=\sqrt{2}(\frac{cosx}{\sqrt{2}}+\frac{sinx}{\sqrt{2}})$
$sinx+cosx=cosx+sinx$