How do you solve 1-sinx=sqrt3cosx?

1 Answer
Nghi N.
Aug 11, 2016

2kpi
pi/3 + 2kpi

Explanation:

1 - sin x = sqrt3cos x
sin x + sqrt3cos x = 1
Call t the arc whose tan t = sqrt3 --> t = pi/3
We get:
sin x + (sin t)/(cos t)cos x = 1
sin x.cos (pi/3) + sin (pi/3).cos x = cos t = 1/2
(sin x + pi/3) = 1/2
Trig table and unit circle give 2 solution arcs:
a. x + pi/3 = pi/3 --> x = 0
b. x + pi/3 = 2pi/3 --> x = (2pi)/3 - pi/3 = pi/3
General answers:
x = 2kpi
x = pi/3 + 2kpi

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