Question

Cos( pi/3+ B) = _____

Answer 1

The required "option A) $\dfrac{1}{2} (\cos B-\sqrt{3}\sin B)$" is correct.

Step-by-step explanation:

We have,

$\cos(\dfrac{\pi}{3}+B)$

To find, the value of $\cos(\dfrac{\pi}{3}+B)$ = ?

∴ $\cos(\dfrac{\pi}{3}+B)$

= $\cos(60+B)$

We know that,

$\cos(A+B)=\cos Acos B-\sin A\sin B$

∴ $\cos(60+B)$

$=\cos 60\cos B-\sin 60\sin B$

= $\dfrac{1}{2} \cos B-\dfrac{\sqrt{3}}{2}\sin B$

Taking $\dfrac{1}{2}$ as common, we get

= $\dfrac{1}{2} (\cos B-\sqrt{3}\sin B)$

Thus, the required "option A) $\dfrac{1}{2} (\cos B-\sqrt{3}\sin B)$" is correct.