How to solve this trigonometric equation? I want to solve the equation (3−cos4x)(sinx−cosx)=2. I solve by putting t=sinx−cosx, but I can not find all solutions.

independanteng

independanteng

Answered question

2022-10-28

How to solve this trigonometric equation?
I want to solve the equation
( 3 cos 4 x ) ( sin x cos x ) = 2.
I solve by putting t = sin x cos x, but I can not find all solutions.

Answer & Explanation

jbaekk7q

jbaekk7q

Beginner2022-10-29Added 18 answers

Use sin x cos x = 2 ( sin ( x π 4 ) ) followed by the substitution x = y + π 4 . You get ( 3 + cos ( 4 y ) ) sin y = 2 . This is satisfied if sin y = 1 2 . The equation ( 3 + cos ( 4 y ) ) sin y = 2 can be written as a fifth-degree polynomial in sin y, and you know one of the roots, so you can get a fourth-degree polynomial.

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