How do you solve # 1 + sin(x) = cos(x)#?

1 Answer
Nghi N.
Jul 1, 2016

Answers: #pi, (3pi)/2#

Explanation:

Use the trig formula:
#sin a - cos a = sqrt2sin (a + pi/4)#
#sin x - cos x = -1#
#sqrt2sin (x + pi/4) = - 1#
#sin (x + pi/4) = - 1/sqrt2 = -sqrt2/2#
Trig table and unit circle -->there are 2 solutions:
a. #x + pi/4 = -pi/4#
#x = - pi/4 - pi/4 = -pi/2#, or #3pi/2# (co-terminal)
b. #x + pi/4 = pi - (-pi/4) = (5pi)/4#
x = #(5pi)/4 - pi/4 = pi#
Answers for #(0, 2pi)#:
#pi, (3pi)/2#
Check .
#x = pi# --> sin x = 0 -> cos x = -1 --> - 1 + 0 = -1 . OK
#x = (3pi)/2# --> sin x = -1 -> cos x = 0 --> -1 + 0 = - 1. OK

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