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

Leland Morrow 2022-06-29 Answered
I need to simplify this expression. I'm not even sure where to start.
tan ( arccos ( x 4 ) )
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Answers (2)

Jovan Wong
Answered 2022-06-30 Author has 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
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varitero5w
Answered 2022-07-01 Author has 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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