How do you express $sin(pi/ 4 ) * sin( ( 23 pi) / 12 )$ without using products of trigonometric functions?

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Answer 1 · 2016-05-26T10:20:58

$-(sqrt3-1)/4$

$sin(pi/4)*sin((23pi)/12)$

$=sin(pi/4)*sin(2pi-pi/12)$

$=-sin(pi/4)*sin(pi/12)$

$=-sin(pi/4)*sqrt(1/2(1-cos(pi/6)$

$=-1/sqrt2*sqrt(1/2(1-sqrt3/2))$

$=-1/sqrt2*sqrt(1/8(4-2sqrt3))$

$=-1/4(sqrt((sqrt3-1)^2))$

$=-1/4(sqrt3-1)$

How do you express sin(pi/ 4 ) * sin( ( 23 pi) / 12 ) sin(pi/ 4 ) * sin( ( 23 pi) / 12 ) without using products of trigonometric functions?