If 20 x = &#x03C0;<!-- π --> , what is cos &#x2061;<!-- ⁡ -->

Makayla Boyd

Makayla Boyd

Answered question

2022-06-10

If 20 x = π, what is cos 4 x cos 8 x cos 4 x cos 8 x ?

Answer & Explanation

pyphekam

pyphekam

Beginner2022-06-11Added 27 answers

20 x = π 10 x = π 2 cos ( 10 x 6 x ) cos ( 10 x 2 x ) cos ( 10 x 6 x ) cos ( 10 x 2 x ) = sin ( 6 x ) sin ( 2 x ) sin ( 6 x ) sin ( 2 x ) = 2 sin ( 2 x ) cos ( 4 x ) sin ( 6 x ) sin ( 2 x ) = 2 cos ( 4 x ) sin ( 6 x ) = 2
sviraju6d

sviraju6d

Beginner2022-06-12Added 6 answers

You have 4 x = π 16 x, so cos 4 x = cos ( π 16 x ) = cos 16 x. By the sum-to-product formula, cos 16 x + cos 8 x = 2 cos 12 x cos 4 x
and we have a first simplification:
cos 4 x cos 8 x cos 4 x cos 8 x = 2 cos 12 x cos 8 x
Now 12 x = π 8 x, so cos 12 x = cos 8 x

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