find the range of this function f(x)=(tan^2(x)−1)/(tan(x))

limunom623

limunom623

Answered question

2022-11-03

I want to find the range of this function.
f ( x ) = tan 2 ( x ) 1 tan ( x )

Answer & Explanation

Prezrenjes0n

Prezrenjes0n

Beginner2022-11-04Added 19 answers

hint
f ( x ) = tan ( x ) 1 tan ( x )
= sin ( x ) cos ( x ) cos ( x ) sin ( x )
= sin 2 ( x ) cos 2 ( x ) sin ( x ) cos ( x )
= 2 cos ( 2 x ) sin ( 2 x )
= 2 tan ( 2 x )
klesstilne1

klesstilne1

Beginner2022-11-05Added 7 answers

We have:
tan 2 ( x ) 1 tan ( x ) = 1 tan x sin 2 x cos 2 x cos 2 x = cos 2 x sin x cos x = 2 cos 2 x sin 2 x = 2 cot 2 x

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