Find all the values of &#x03B8;<!-- θ --> that satisfy cos &#x2061;<!-- ⁡ --> (

Craig Mendoza

Craig Mendoza

Answered question

2022-06-24

Find all the values of θ that satisfy cos ( x θ ) + cos ( ( x + 2 ) θ ) = cos ( θ )

Answer & Explanation

Samantha Reid

Samantha Reid

Beginner2022-06-25Added 22 answers

it's
2 cos ( x + 1 ) θ cos θ = cos θ
or
( 2 cos ( x + 1 ) θ 1 ) cos θ = 0.
Can you end it now?
Actually, cos θ = 0 gives
θ = π 2 + π k ,
where k Z
Also, there is a mistake in your second sequence.
I used
cos α + cos β = 2 cos α + β 2 cos α β 2
and
π = 180 .
Winigefx

Winigefx

Beginner2022-06-26Added 4 answers

Use
cos ( p ) + cos ( q ) = 2 cos ( p + q 2 ) cos ( p q 2 )
Make p = ( x + 2 ) θ and q = x θ making your problem to be
2 cos ( ( x + 1 ) θ ) cos ( θ ) = cos ( θ )
and then the two cases.

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