Please, can anyone help me with this help to solve this question?. Verify that each x-value is a solution of the equation. 3 tan^2(5x) − 1 = 0. (a) x = pi/30 (b) x =5pi/30

Please help to solve this question.
Verify that each x-value is a solution of the equation.
3 tan^2(5x) − 1 = 0.
(a) x = pi/30
(b) x =5pi/30

1 Answer
Jun 12, 2018

x = pi/30 + (kpi)/5
x = (5pi)/30 + (kpi)/5

Explanation:

3tan^2 (5x) = 1
tan^2 (5x) = 1/3
tan (5)x = +- sqrt3/3
a. tan (5x) = sqrt3/3
Trig table and unit circle give:
5x = pi/6 + kpi
x = pi/30 + (kpi)/5
b. tan (5x) = - sqrt3/3
5x = (5pi)/6 + kpi
x = (5pi)/30 + ( kpi)/5
Verification
x = pi/30 --> 5x = pi/6 -->
3tan^2 (pi/6) = 3(1/sqrt3)^2 = 1. Proved
x = (5pi)/30 = pi/6 --> 5x = (5pi)/6 -->
3tan^2(5pi/6) = 3(1/sqrt3)^2 = 1. Proved