Question

1/2(cosa+√3sina)=cos(60˚-a)

Answer 1

$\dfrac{1}{2} (\text{cos}\ a + \sqrt{3} \ \cdotp \text{sin}\ a) = \text{cos} (60^{\circ} - a) \\\\\dfrac{1}{2} \text{cos}\ a + \dfrac{\sqrt{3}}{2} \ \cdotp \text{sin}\ a = \text{cos} \bigg(\dfrac{\pi}{3} - a \bigg)\\\\\text{cos}\bigg(\dfrac{\pi}{3} \bigg) \text{cos} \ a + \text{sin}\bigg(\dfrac{\pi}{3} \bigg) \text{sin} \ a = \text{cos} \bigg(\dfrac{\pi}{3} - a \bigg)\\\\\text{cos}\bigg(\dfrac{\pi}{3} - a \bigg) = \text{cos}\bigg(\dfrac{\pi}{3} - a \bigg)$

$a \in R$

$\text{OTBET:} \ a \in R$