Proving 6 sec &#x2061;<!-- ⁡ --> &#x03D5;<!-- ϕ --> tan &#x2061;<!-- ⁡ --> &#x

Reed Eaton

Reed Eaton

Answered question

2022-06-26

Proving 6 sec ϕ tan ϕ = 3 1 sin ϕ 3 1 + sin ϕ

Answer & Explanation

Reagan Madden

Reagan Madden

Beginner2022-06-27Added 15 answers

sec ϕ tan ϕ = sin ϕ cos 2 ϕ = sin ϕ 1 sin 2 ϕ = sin ϕ ( 1 + sin ϕ ) ( 1 sin ϕ ) = sin ϕ 1 2 sin ϕ ( 1 1 sin ϕ 1 1 + sin ϕ ) = 1 2 ( 1 1 sin ϕ 1 1 + sin ϕ )
Emanuel Keith

Emanuel Keith

Beginner2022-06-28Added 8 answers

Notice that
3 1 sin ϕ 3 1 + sin ϕ = 3 + 3 sin ϕ 3 + 3 sin ϕ 1 sin 2 ϕ
using 1 sin 2 ϕ = cos 2 ϕ, We get
6 sin ϕ cos 2 ϕ = 6 sin ϕ ( cos ϕ ) ( cos ϕ )
6 sec ϕ tan ϕ

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