Logarithms with trigonometric inequality log_(tg(x))sqrt(sin(x)^2-5/12)<1

garkochenvz

garkochenvz

Answered question

2022-08-11

Logarithms with trigonometric inequality
My class is going to have an exam tomorrow, but we can't figure out how to solve such equations.
log   t g ( x ) sin ( x ) 2 5 / 12 < 1
We tried to transform 1 to log   t g ( x ) t g ( x ) and solve it as
sin ( x ) 2 5 / 12 < t g ( x )
But we don't know how to continue. Any help will be greatly appreciated.

Answer & Explanation

Kelton Glover

Kelton Glover

Beginner2022-08-12Added 17 answers

Square both sides, replace tan x with sin x cos x , and cos 2 x with 1 sin 2 x

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