Sine of x plus Cosine of x

Theorem

Sine Form

$\sin x + \cos x = \sqrt 2 \sin \left({x + \dfrac \pi 4}\right)$

Cosine Form

$\sin x + \cos x = \sqrt 2 \, \map \cos {x - \dfrac \pi 4}$

Also see

• Sine of x minus Cosine of x
• Cosine of x minus Sine of x