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

Isa Trevino

Isa Trevino

Answered question

2021-09-16

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

Answer & Explanation

svartmaleJ

svartmaleJ

Skilled2021-09-17Added 92 answers

Step 1
Given equation is,
2sin(2x)sin(x)=2cos(x)
Step 2
Now,
2sinxcosxsinxcosx=1
2sin2x=1
sin2x=12
sinx=±12
Step 3
Then the values of x,
x=nπ+(1)nπ4
at n=0
x=π4
at n=1
x=ππ4=3π4
Therefore, values of x in the interval [0,2π) are,
x=π4,3π4

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