The value 105^ + 105^ is - Vidyadip

MCQ

The value $\cos 105^\circ + \sin 105^\circ $ is

A
$\frac{1}{2}$
B
$1$
C
$\sqrt 2 $
✓
$\frac{1}{{\sqrt 2 }}$

✓

Answer

Correct option: D.

$\frac{1}{{\sqrt 2 }}$

d
(d) $\cos 105^\circ + \sin 105^\circ = \cos (90^\circ + 15^\circ ) + \sin (90^\circ + 15^\circ )$

$= \cos 15^\circ - \sin 15^\circ $

$= \frac{{\sqrt 3 + 1}}{{2\sqrt 2 }} - \frac{{\sqrt 3 - 1}}{{2\sqrt 2 }} $

$= \frac{2}{{2\sqrt 2 }} = \frac{1}{{\sqrt 2 }}$.

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