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Rachel Ross

Rachel Ross

Answered question

2022-06-03

Solve 2 cos 2 x = 3 sin 2 x and give the sum of all the solutions in the interval 0 x 2 π ..

Answer & Explanation

gsoublogpycv8

gsoublogpycv8

Beginner2022-06-04Added 3 answers

Using the fact that sin 2 θ = 2 cos θ sin θ on the RHS I get
2 cos 2 x = 2 3 cos x sin x .
The right way to solve is:
2 cos 2 x = 2 3 cos x sin x cos x ( cos x 3 sin x ) = 0
what give you:
cos x = 0  or  cos x 3 sin x = 0
For
cos x = 0 x = π 2 + k π
and for,
cos x 3 sin x = 0 tan x = 3 3 x = π 6 + k π

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