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

Chesley

Chesley

Answered question

2021-09-20

Solve the equation. (Find all solutions of the equation in the interval [0, 2π).
6tan(2x)6cot(x)=0

Answer & Explanation

Layton

Layton

Skilled2021-09-21Added 89 answers

Step 1
Consider the given equation:
6tan(2x)6cotx=0
Add 6cotx on both sides:
6tan(2x)6cotx+6cotx=6cotx
6tan(2x)=6cotx
Divide equation by 6 on both side:
6tan(2x)6=6cotx6
tan(2x)=cotx
Step 2
We know that,
tan(2x)=2tanx1tan2x
Therefore,
2tanx1tan2x=1tanx
2tan2x1tan2x=1
2tan2x=1tan2x
tan2x=13
tanx=13
Hence, x=π6,7π6

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