# How do I go about completing the identity?

### 2 Answers

Relevance

- ?Lv 73 weeks ago
cos (x - 11π/6) = cos x cos 11π/6 + sin x sin 11π/6

........................= (cos x)(√3/2) + (sin x)(-1/2)

........................= 1/2 [ √3 cos x - sin x ]...............ANS

- husoskiLv 73 weeks ago
The simplest way is to use the cosine-of-a-difference identity:

cos (A - B) = (cos A)(cos B) + (sin A)(sin B)

With B = 11*pi/6,

cos B = cos (2pi - B) = cos (pi/6) = sqrt(3)/2

sin B = - sin (2pi - B) = - sin (pi/6) = -1/2

So cos (x - 11pi/6) = (sqrt(3)/2) cos x - (1/2) sin x, after substituting and simplfying.

Still have questions? Get your answers by asking now.