Solving sin 2 </msup> &#x2061;<!-- ⁡ --> x + sin 2 </msu

hetriamhageh6k20

hetriamhageh6k20

Answered question

2022-05-15

Solving sin 2 x + sin 2 2 x sin 2 3 x sin 2 4 x = 0

Answer & Explanation

recajossikpfmq

recajossikpfmq

Beginner2022-05-16Added 19 answers

First linearise with:
sin 2 u = 1 cos 2 u 2 .
Simplifying yields the equation
cos 2 x + cos 4 x = cos 6 x + cos 8 x .
Then the factorisation formula:
cos p + cos q = 2 cos p + q 2 cos p q 2
lets you rewrite the equation, after some simplification, as
cos x cos 3 x = cos x cos 7 x { cos x = 0 or cos 3 x = cos 7 x .
Solutions to the first equation: x π 2 mod π
Solutions to the second equation:
7 x ± 3 x mod 2 π { 4 x 0 mod 2 π 10 x 0 mod 2 π { x 0 mod π 2 x 0 mod π 5
The solutions in the second series are redundant either with the first or the third series. The set of solutions can ultimately be described as:
x π 2 mod π , x 0 mod π 5 .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?