Simplify the following question

Question

I need help Solving or Simplifying this equation in trigonometry cos(x+pi/3) in

Answer 1

Using the cosine of the sum of angles identity...

cos(x + ^π/₃) = cos(x)⋅cos(^π/₃) - sin(x)⋅sin(^π/₃)

= cos(x)⋅(¹/₂) - sin(x)⋅(^√3/₂) (evaluate the cos(^π/₃) & sin(^π/₃) )

= (¹/₂)⋅[ cos(x) - sin(x)⋅(√3) ] (factor out ¹/₂)

= (¹/₂)⋅[ cos(x) - √3⋅sin(x) ] (move √3 to be

a coëfficient for

the sin(x) term)