Find the general solution to cos2x=-cosx

Caelan

Caelan

Answered question

2021-02-11

Find the general solution to cos2x=cosx

Answer & Explanation

jlo2niT

jlo2niT

Skilled2021-02-12Added 96 answers

cos(2x)=2cos2(x)1
2cos2(x)1=cos(x)
2cos2(x)1cos(x)=0
2cos2(x)cos(x)1=0
(2cos(x)+1)(cos(x)1)=0
2cos(x)+1=0
2cos(x)=1
cos(x)=12
x=cos1(12)
x=π/3[2ππ/3=5π/3]
x=π/3 and 5π/3
In the first and fourth quadrants, cos is positive.
cos(x)1=0
cos(x)=1
x=cos1(1)
x=0,2π

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