How do you express $sin(pi/12) * cos(( 13 pi)/12 )$ without products of trigonometric functions?

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Answer 1 · 2018-07-03T09:12:07

$color(red)(-sin (pi/6)= -1/2$

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$sin (pi/12) * cos ((13pi)/12)$

$sin x cos y = (1/2)[sin(x+y) + sin (x-y])$

$=> (1/2)[sin (pi/12 + (13pi)/12) + sin (pi/12 - (13pi)/12)]$

$=> [sin ((14pi)/12) + sin (-pi)]/2$

$=> [sin (pi + pi/6) - sin (pi)]/2$

$color(red)(-sin (pi/6)= -1/2$

How do you express sin(pi/12) * cos(( 13 pi)/12 ) sin(pi/12) * cos(( 13 pi)/12 ) without products of trigonometric functions?