How do you express $sin (\frac{π}{4}) \cdot sin (\frac{π}{8})$ $sin(pi/ 4 ) * sin( ( pi) / 8 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{π}{8})$ $sin(pi/ 4 ) * sin( ( pi) / 8 )$ without using products of trigonometric functions?

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Answer 1 · 2017-06-10T11:29:10

$\frac{\sqrt{2} \cdot \sqrt{2 - \sqrt{2}}}{4}$ $(sqrt2*sqrt(2-sqrt2))/4$

Explanation:

Use the identity: $sin (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ $sin(pi/4)=(sqrt2)/2$

$sin (\frac{π}{8}) = \sqrt{\frac{2 - \sqrt{2}}{4}}$ $sin(pi/8)=sqrt((2-sqrt2)/4)$

Hence,

$sin (\frac{π}{4}) \cdot sin (\frac{π}{8}) = \frac{\sqrt{2}}{2} \cdot \sqrt{\frac{2 - \sqrt{2}}{4}}$ $sin(pi/4)*sin(pi/8)=(sqrt2)/2*sqrt((2-sqrt2)/4)$
$\times \times \times \times \times x . = \frac{\sqrt{2} \cdot \sqrt{2 - \sqrt{2}}}{4}$ $color(white)(xxxxxxxxxxx.)=(sqrt2*sqrt(2-sqrt2))/4$

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{π}{8})$ $sin(pi/ 4 ) * sin( ( pi) / 8 )$ without using products of trigonometric functions?

1 Answer

Explanation:

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{π}{8})$ $sin(pi/ 4 ) * sin( ( pi) / 8 )$ without using products of trigonometric functions?