Question #c6dcd

1 Answer
Mar 19, 2017

x = 2kpi
x = pi/2 + 2kpi.

Explanation:

Use trig identity:
sin x + cos x = sqrt2sin (x + pi/4)
In this case:
sin x + cos x = sqrt2sin (x + pi/4) = 1
sin (x + pi/4) = 1/sqrt2 = sqrt2/2
Two solutions:
(x + pi/4) = pi/4 + 2kpi, and (x + pi/4) = (3pi)/4 + 2kpi
a. x + pi/4 = pi/4 + 2kpi
x = 0 + 2kpi
b. x + pi/4 = (3pi)/4 + 2kpi
x = (3pi)/4 - pi/4 = pi/2 + 2kpi.

Check.
x = 0 --> sin o = 0 --> cos 0 = 1 --> 0 + 1 = 1 OK
x = pi/2 --> sin (pi/2) = 1 --> cos (pi/2) = 0 --> 1 + 0 = 1. OK