3 years ago

Need help with number 5

Mathematics

1 answer:

uysha [10]3 years ago

5 0

Answer:

gxhxf

Step-by-step explanation:

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Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2

Oxana [17]

Answer:

The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Step-by-step explanation:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$

Multiply and Divide by $2cos(\frac{\pi }{14})$

= $\frac{2sin(\frac{\pi }{14})cos(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})}{2cos(\frac{\pi }{14})}$

⇒ Let $\frac{\pi }{14}$ = Ф and 7Ф = $\frac{\pi }{2}$

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ ∵cos7Ф = 0

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ ∵sin7Ф = 1

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Keywords: prove, sinФ, cosФ

Learn more about trigonometric functions from brainly.com/question/7331447

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