The value of 105^ + 105^ is - Vidyadip

MCQ

The value of $\cos105^{\circ}+\sin105^{\circ}$ is

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

✓

Answer

Correct option: D.

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

(D)
$\cos105^{\circ}+\sin105^{\circ}$
$=\cos\left(90^{\circ}+15^{\circ}\right)+\sin\left(90^{\circ}+15^{\circ}\right)$
$=\cos15^{\circ}-\sin15^{\circ}$
$=\cos\left(45^{\circ}-30^{\circ}\right)-\sin\left(45^{\circ}-30^{\circ}\right)$
$=\frac{\sqrt{3+1}}{2\sqrt{2}}-\frac{\sqrt{3-1}}{2\sqrt{2}}$
$=\frac{2}{2\sqrt{2}}$
$=\frac{1}{\sqrt{2}}$

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