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How do you express $sin(pi/ 4 ) * sin( ( pi) / 8 )$ without using products of trigonometric functions?

1 Answer

Jun 10, 2017

$(sqrt2*sqrt(2-sqrt2))/4$

Explanation:

Use the identity: $sin(pi/4)=(sqrt2)/2$

$sin(pi/8)=sqrt((2-sqrt2)/4)$

Hence,

$sin(pi/4)*sin(pi/8)=(sqrt2)/2*sqrt((2-sqrt2)/4)$
$color(white)(xxxxxxxxxxx.)=(sqrt2*sqrt(2-sqrt2))/4$

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