Find tan ⁡ ( α + β ) when tan ⁡ β = n sin...

Patatiniuh

Patatiniuh

Answered

2022-07-09

Find tan ( α + β ) when tan β = n sin α cos α 1 n cos 2 α

Answer & Explanation

SweallySnicles3

SweallySnicles3

Expert

2022-07-10Added 21 answers

I think it will be easier if one first simplifies tan β,
tan β = n sin α cos α 1 n cos 2 α = n tan α 1 / cos 2 α n = n tan α tan 2 α + 1 n .
Next, use the addition formula for tan ( α + β ) and insert the expression above everywhere you encounter tanβ. Simplify, and you got your result.

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