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

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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
Nghi N.
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

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