5sinx=5sqrt3cosx 0<x<2pi What are all possible solutions?

1 Answer
Oct 25, 2015

solve 5sin x = 5sqrt3cos x

Ans: pi/3 and (4pi)/3

Explanation:

There are two ways.
1. First way. Divide both side by 5cos x (condition cos x != 0, or x != pi/2 and x !=3pi/2)
tan x = sqrt3 --> x = pi/3 and x = pi/3 + pi = (4pi)/3
2. Second way. Simplify both sides by 5
sin x - sqrt3cos x = 0
Replace in the equation (sqrt3) by tan (pi)/3 = (sin (pi/3)/(cos pi/3))
sin x.cos ((pi)/3) - sin ((pi)/3).cos x = 0
sin (x - pi/3) = 0
(x - pi/3) = 0 --> x = pi/3 and (x - pi/3) = pi --> x = pi + pi/3 = (4pi)/3#