Solve the equation. (Find all solutions of the equation in the interval

Joni Kenny

Joni Kenny

Answered question

2021-09-14

Solve the equation. (Find all solutions of the equation in the interval (0, 2π).
cos(2x)cos(x)=0

Answer & Explanation

Malena

Malena

Skilled2021-09-15Added 83 answers

Step 1
The given equation is,
cos(2x)cos(x)=0
Step 2
Use the trigonometric identity to solve the equation.
cos(2x)cos(x)=0
2cos2(x)1cosx=0
2cos2(x)cosx1=0
2u2u1=0 ( Assume u=cosx)
2u22u+u1=0
2u(u-1)+1(u-1)=0
(2u+1)(u-1)=0
u=12,1
Step 3
Replace u by cosx.
cosx=12 and cosx=1
x=cos1(12) and x=cos1(1)
x=2π3,4π3 and x=0
x=0,2π3,4π3

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