How do you solve #cosx=sinx# and find all exact general solutions?

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How do you solve #cosx=sinx# and find all exact general solutions?

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Answer 1 · 2016-07-22T02:45:21

#x = pi/4 + 2kpi#

Explanation:

cos x = sin x
Property of complementary arcs -->
#cos x = sin (pi/2 - x)#
There for:
sin x = sin (pi/2 - x)
There are 2 solutions:
a. #x = pi/2 - x# --> #2x = pi/2# --> #x = pi/4#
b. #x = pi - (pi/2 - x) = pi/2 + x#
Undefined equation .
General answer:
#x = pi/4 + 2kpi#

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How do you solve #cosx=sinx# and find all exact general solutions?

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