Question

How do you simplify `cos( pi + x) + cos (pi - x)`?

Answer 1

2cos x

Explanation:

Apply the trig identity:
`cos a + cos b = 2cos ((a + b)/2).cos ((a - b)/2)`
`S = cos (pi + x) + cos (pi - x) = 2cos (pi).cos (- x)`
Since `cos pi = - 1` and `cos (- x) = cos x`, therefor
S = - 2cos x