Double angle formulae for sin &#x2061;<!-- ⁡

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Answered question

2022-06-04

Double angle formulae for sin 2 θ and cos 2 θ in tangent form?

Answer & Explanation

Jakobe Yang

Jakobe Yang

Beginner2022-06-05Added 5 answers

Using tan ( θ ) = sin ( θ ) cos ( θ )
2 tan ( θ ) 1 + tan 2 ( θ ) = 2 tan ( θ ) 1 1 1 + tan 2 ( θ ) = 2 sin ( θ ) cos ( θ ) 1 1 + tan 2 ( θ )
Now
1 + tan 2 ( θ ) = 1 + sin 2 ( θ ) cos 2 ( θ ) = cos 2 ( θ ) + sin 2 ( θ ) cos 2 ( θ ) = 1 cos 2 ( θ )
In the first equation, changing this value
2 tan ( θ ) 1 + tan 2 ( θ ) = 2 sin ( θ ) cos ( θ ) 1 1 + tan 2 ( θ ) = 2 sin ( θ ) cos ( θ ) cos 2 ( θ ) 1 = 2 sin ( θ ) cos ( θ ) = sin ( 2 θ )
Go through a similar process for cos ( 2 θ ) .
Payton Salazar

Payton Salazar

Beginner2022-06-06Added 3 answers

sin 2 θ = 2 sin θ cos θ = 2 sin θ cos θ cos 2 θ + sin 2 θ = 2 tan θ 1 + tan 2 θ
cos 2 θ = cos 2 θ sin 2 θ = cos 2 θ sin 2 θ cos 2 θ + sin 2 θ = 1 tan 2 θ 1 + tan 2 θ

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