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3 years ago

Hello! Please help!! I really need this.

Mathematics

2 answers:

Liono4ka [1.6K]3 years ago

7 0

Answer:

Lets show that:

cos x cos 2x cos 4x cos 8x = sin 16x / 16 sinx

Use formula:

sin 2x = 2 sin x cos x

Multiply LHS by 2sinx/2sinx:

2sinx cos x cos 2x cos 4x cos 8x / 2 sin x =
sin 2x cos 2x cos 4x cos 8x / 2 sin x =
2sin 2x cos 2x cos 4x cos 8x / 4 sin x =
sin 4x cos 4x cos 8x / 4 sin x =
2sin 4x cos 4x cos 8x / 8 sin x =
sin 8x cos 8x / 8 sin x =
2 sin 8x cos 8x / 16 sin x =
sin 16x / 16 sin x

Now, we can easily find that:

sin (16*2π/15) = sin (2π/15)

Coming back to the original equation, we get:

cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = sin (16*2π/15) / 16 sin (2π/15)
cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = 1/16

IrinaVladis [17]3 years ago

4 0

its a i did this a while ago

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3 years ago

Hello! Please help!! I really need this.​

Hello! Please help!! I really need this.