How do you express $sin (\frac{π}{4}) \cdot sin (\frac{23 π}{12})$ $sin(pi/ 4 ) * sin( ( 23 pi) / 12 )$ without using products of trigonometric functions?

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Answer 1 · 2016-05-26T10:20:58

$- \frac{\sqrt{3} - 1}{4}$ $-(sqrt3-1)/4$

$sin (\frac{π}{4}) \cdot sin (\frac{23 π}{12})$ $sin(pi/4)*sin((23pi)/12)$

$= sin (\frac{π}{4}) \cdot sin (2 π - \frac{π}{12})$ $=sin(pi/4)*sin(2pi-pi/12)$

$= - sin (\frac{π}{4}) \cdot sin (\frac{π}{12})$ $=-sin(pi/4)*sin(pi/12)$

$= - sin (\frac{π}{4}) \cdot \sqrt{\frac{1}{2} (1 - cos (\frac{π}{6})}$ $=-sin(pi/4)*sqrt(1/2(1-cos(pi/6)$

$= - \frac{1}{\sqrt{2}} \cdot \sqrt{\frac{1}{2} (1 - \frac{\sqrt{3}}{2})}$ $=-1/sqrt2*sqrt(1/2(1-sqrt3/2))$

$= - \frac{1}{\sqrt{2}} \cdot \sqrt{\frac{1}{8} (4 - 2 \sqrt{3})}$ $=-1/sqrt2*sqrt(1/8(4-2sqrt3))$

$= - \frac{1}{4} (\sqrt{{(\sqrt{3} - 1)}^{2}})$ $=-1/4(sqrt((sqrt3-1)^2))$

$= - \frac{1}{4} (\sqrt{3} - 1)$ $=-1/4(sqrt3-1)$

How do you express sin(pi/ 4 ) * sin( ( 23 pi) / 12 ) sin(π4)⋅sin(23π12)sin(pi/ 4 ) * sin( ( 23 pi) / 12 ) without using products of trigonometric functions?