Reduce each of the following expressions to the sine or cosine of a single expression: `sqrt(3)sintheta-costheta`

Explanation

Suppose `f(theta) = sqrt(3) sin theta – cos theta`

On dividing and multiplying by `sqrt(((sqrt(3))^2 + 1^2))` i.e. by 2


`f(theta) = 2((sqrt(3))/2 sin theta – 1/2 cos theta)`

f(theta) = `2(cos (pi/6) sin theta – sin (pi/6) cos theta) `

As we know that, `sin A cos B – cos A sin B = sin (A – B)`

`f(theta) = 2 sin (theta – pi/6) `