akar(2) cos (pi/4-x) =

$\cos(x) + \sin(x)$

Pembahasan

Untuk menyederhanakan ekspresi $\sqrt{2} \cos(\pi/4 - x)$, kita dapat menggunakan identitas penjumlahan atau pengurangan kosinus:
$\,\cos(A - B) = \cos A \cos B + \sin A \sin B$

Dalam kasus ini, $A = \pi/4$ dan $B = x$.
$\,\cos(\pi/4 - x) = \cos(\pi/4) \cos(x) + \sin(\pi/4) \sin(x)$

Kita tahu bahwa $\cos(\pi/4) = \sqrt{2}/2$ dan $\sin(\pi/4) = \sqrt{2}/2$.
$\,\cos(\pi/4 - x) = (\sqrt{2}/2) \cos(x) + (\sqrt{2}/2) \sin(x)$
$\,\cos(\pi/4 - x) = (\sqrt{2}/2) (\cos(x) + \sin(x))$

Sekarang, kita kalikan dengan $\sqrt{2}$:
$\,\sqrt{2} \cos(\pi/4 - x) = \sqrt{2} \times (\sqrt{2}/2) (\cos(x) + \sin(x))$
$\,\sqrt{2} \cos(\pi/4 - x) = (2/2) (\cos(x) + \sin(x))$
$\,\sqrt{2} \cos(\pi/4 - x) = 1 (\cos(x) + \sin(x))$
$\,\sqrt{2} \cos(\pi/4 - x) = \cos(x) + \sin(x)$

Jadi, $\sqrt{2} \cos(\pi/4 - x) = \cos(x) + \sin(x)$.