Find the solution of the equation in the interval 0^{0}\leq x < 360^{0}.

Efan Halliday

Efan Halliday

Answered question

2021-09-12

Find the solution of the equation in the interval 00x<3600.
2cos2x5cosx=3

Answer & Explanation

Malena

Malena

Skilled2021-09-13Added 83 answers

Step 1
It is given that, 2cos2x5cosx=3
We have to find the solution of the equation in the interval 00x<3600.
Step 2
We have, 2cos2x5cosx=3
2cos2x(61)cosx3=0
2cos2x6cosx+1cosx3=0
2cosx(cosx3)+1(cosx3)=0
(cosx3)(2cosx+1)=0
(cosx3)=0 or (2cosx+1)=0
cosx=3 or cosx=12
x=4π3 or x=2π3
x=240 or x=120
Hence, x=120,240

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-27Added 2605 answers

Answer is given below (on video)

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