Question

The equation sin ( (PI/3) - x ) is equal to ____.
A. 1/2( sqrt(3) cosx + sinx)
B. 1/2(sqrt(3) cosx - sinx)
C. 1/2(cosx- sqrt(3) sinx)
D. 1/2 (cosx + sqrt(3) sinx)

Answer 1

sin ( π / 3 - x ) =
= sin π/3 cos x - cos π/3 sin x =    ( additional formulas )
= √3 / 2 cos x - 1/2 sin x =
= 1/2 ( √3 cos x - sin x )
Answer: B )

Answer 2

Answer:

The Value of

$Sin (\frac{\pi}{3}-x)=Sin(\frac{\pi}{3})*cos x - Cos(\frac{\pi}{3})* Sin x\\\\=\frac{\sqrt{3}}{2}*Cos x -\frac{Sin x}{2}\\\\=\frac{1}{2}[\sqrt{3}Cos x - Sin x]$

Using the Sine Law

Sin (A-B)=Sin A *Cos B - Cos A * Sin B

as well as

$Sin (\frac{\pi}{3})=\frac{\sqrt{3}}{2}, Cos (\frac{\pi}{3})=\frac{1}{2}$

Option B: $\frac{1}{2}[\sqrt{3}Cos x - Sin x]$