Question #38271

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Question #38271

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Answer 1 · 2017-04-08T02:37:10

#pi/4#

Explanation:

sin x - cos x = 0
Use trig identity:
#sin x - cos x = sqrt2sin (x - pi/4)#
#sqrt2sin (x - pi/4) = 0#
#sin (x - pi/4) = 0#
Unit circle gives 3 solutions:
a. #(x - pi/4) = 0# --> #x = pi/4#
b. #x - pi/4 = pi #--> #x = pi + pi/4 = (5pi)/4# (out of interval)
c. #x - pi /4 = 2pi# --> #x = 2pi + pi/4 = (9pi)/4 = pi/4#

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Question #38271

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