Help for this equation Can anyone show me how to solve this trignometric equation : sin(2 theta)-cos(2 theta)=1/2

Emilio Calhoun

Emilio Calhoun

Answered question

2022-10-30

Help for this equation
Can anyone show me how to solve this trignometric equation :
sin ( 2 θ ) cos ( 2 θ ) = 1 2

Answer & Explanation

Shyla Larson

Shyla Larson

Beginner2022-10-31Added 11 answers

HINT
Let use
cos 2 θ = 1 t 2 1 + t 2
sin 2 θ = 2 t 1 + t 2
where
t = tan θ
and solve for t, that is
t 2 + 4 t 3 = 0
Dylan Nixon

Dylan Nixon

Beginner2022-11-01Added 2 answers

It's
sin ( 2 θ π 4 ) = 1 2 2
and the rest is smooth:
2 θ π 4 = ( 1 ) n arcsin ( 1 2 2 ) + π n ,
where n is integer or
θ = π 8 + ( 1 ) n 1 2 arcsin ( 1 2 2 ) + π n 2 .

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