Solve 2 sin ⁡ x cos ⁡ x = 1 + 3 tan ⁡ x

fythynwyrk0

fythynwyrk0

Answered

2022-07-13

Solve 2 sin x cos x = 1 + 3 tan x

Answer & Explanation

isscacabby17

isscacabby17

Expert

2022-07-14Added 13 answers

Note that tan x + cot x = sin x cos x + cos x sin x = 1 sin x cos x (this is something I've filed away from seeing it in a lot of "verify this trig identity" type problems) .
So your equation can be written 2 ( tan x + cot x ) = 1 + 3 tan x, or
2 ( tan x + 1 tan x ) = 1 + 3 tan x .
Now that everything is in terms of tangent, you should be able to get it into the form of an equation that's quadratic in tan x (i.e., has multiples of tan 2 x , tan x ,, and a number) and solve; the values of tanx are nice integers, although you will need inverse trig to get one of the x-values.

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