Find the exact value of the expression.?

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Answer 1 · 2018-02-21T13:35:26

#=> color(green)(1/2)#

#sin(pi/4) cos(pi/12) + cos(pi/4) sin (pi/12)#

It is in the form #sin a * cos b + cos a * sin b#

where #a = pi / 4, b = pi / 12#

But # sin (a + b) = sin a * cos b + cos a * sin b # (an identity)

#:. (sin (pi/4) * cos (pi/12) + cos(pi/4) * sin (pi/12))#

#=> sin ((pi/4) + (pi/12))#

#=> sin ((3pi + pi) / 12) = sin( (cancel(4)pi)/ cancel(12)^color(brown) (3)) = sin (pi/3) = color(green)(1/2)#