Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function. Given: displaystyle tan{{left({{cos}^{ -{{1}}}{5}}{x}right)}}=?

Wribreeminsl 2021-02-25 Answered
Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function.
Given:
tan(cos15x)=?
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Expert Answer

joshyoung05M
Answered 2021-02-26 Author has 97 answers
Step 1
Let,
a=cos15x
Then, cosa=5x
Therefore,
sin2a+cos2a=1
sin2a=1cos2a
sina=±1cos2a
sina=±1(5x)2
sina=±125x2
Step 2
Hence,
tan(cos15x)=tana
=sinacosa
tan(cos15x)=±125x25x
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Jeffrey Jordon
Answered 2021-10-25 Author has 2064 answers

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