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Answer 1 · 2016-10-31T03:32:24

$(sin5pi)/12 = (sqrt6 - sqrt2) / 4$

This requires intermediate algebra skills.

We are simply stating this in another way:

$(sin5pi)/12 = sin (π/4 + π/6)$

Using an identity ( $cos (a + b) = cos a cos b - sin a sin b$ ) to represent this so that we can use more to simplify them afterwards:

$cos(pi/6 + pi/4) =(cospi/4)( cos pi/6) + (sinpi/4)( sin pi/6)$

Now we can simply substitute the values we memorized to this:

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

Therefore, we can state that:

$=sqrt6 / 4 - sqrt2 / 4$

Thus,

$:. (sqrt6 - sqrt2) / 4$

Hope this helped :)!