Question

How do you prove `cos(pi/3 + x) + cos(pi/3 - x) = cosx`?

Answer 1

Prove trig expression.

Explanation:

Apply the trig identity:
`cos a + cos b = 2cos ((a + b)/2).cos ((a - b)/2)`
Sum `S = cos (pi/3 + x) + cos (pi/3 - x) = 2cos (pi/3).cos x`
Trig table gives --> `cos (pi/3) = 1/2`. Therefor,

S = cos x