How do you express #sin(pi/ 4 ) * sin( ( 3 pi) / 8 ) # without using products of trigonometric functions?

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How do you express #sin(pi/ 4 ) * sin( ( 3 pi) / 8 ) # without using products of trigonometric functions?

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Answer 1 · 2018-07-01T09:59:11

#color(maroon)(=> (sin ((5pi)/8) - sin (pi/8)) / 2#

Explanation:

![https://lo.wikipedia.org/wiki/%E0%BB%84%E0%BA%95%E0%BA%A1%E0%BA%B8%E0%BA%A1]( useruploads.socratic.org )

#sin A * sin B = (1/2) * (sin (A+B) + sin (A-B)), Identity#

#sin (pi/4) * sin((3pi)/8)#

#=> (1/2) * (sin (pi/4 + (3pi)/8) + sin (pi/4 - (3pi) / 8)#

#=.> (1/2) (sin ((5pi)/8) + sin -(pi/8))#

#color(maroon)(=> (sin ((5pi)/8) - sin (pi/8)) / 2#

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How do you express #sin(pi/ 4 ) * sin( ( 3 pi) / 8 ) # without using products of trigonometric functions?

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