How do I find all the solutions of 'sin^2(x) = 1-cosx' in terms of radians from zero to 2pi?

Question

Find all solutions of the equation in the interval [0, 2pi]

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Answer 1 · 2018-04-19T03:20:54

0, #pi/2#, #(3pi)/2#

#sin^2x=1-cosx#

#1-cos^2x=1-cosx#

#-cos^2x+cosx=0#

#cos^2x-cosx=0# Multiplying both sides by -1

#cosx(cosx-1)=0# Factoring the left side

Set sides equal to zero

Cosx=0

or

Cosx-1=0
Cosx=1

Find instances where cosx is equal to '1' and '0'

Answers: 0, #pi/2#, #(3pi)/2#