I need to simplify this expression. I'm not even sure where to start. tan &#x2061;<!-- ⁡ --

Leland Morrow

Leland Morrow

Answered question

2022-06-29

I need to simplify this expression. I'm not even sure where to start.
tan ( arccos ( x 4 ) )

Answer & Explanation

Jovan Wong

Jovan Wong

Beginner2022-06-30Added 23 answers

Let y = tan ( cos 1 ( x 4 ) ) , , Now Put cos 1 ( x 4 ) = ϕ ,
Then x 4 = cos ϕ , , Then sec ϕ = 4 x , , So using tan ϕ = ± sec 2 ϕ 1 = ± 16 x 2 x
So We get y = tan ϕ = ± 16 x 2 x
varitero5w

varitero5w

Beginner2022-07-01Added 6 answers

Let arccos x 4 = θ
This implies
x 4 = cos θ
Forming a right angled triangle with the above and using pythagoras' theorem, opposite side to angle θ will be: ± 16 x 2
Therefore,
tan θ = tan ( arccos x 4 ) = 16 x 2 x

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