Question

How do you solve `(cos2x)(cos(pi/3)) + (sin2x)(sin(pi/3)) = (sqrt(3))/2`, where domain is [0,2pi]?

Answer 1

Use the trig identity: cos (a - b) = cos a.cos b + sin a.sin b

`cos (2x - Pi/3) = (sqrt3)/2 = cos +- (pi/6)`

a.`2x - pi/3 = pi/6 -> 2x = (3pi)/6 = pi/2 -> x = pi/4`

b. `2x - pi/3 = (11pi)/6 -> 2x = (13pi)/6 -> x = (13pi)/12`