How do you evaluate $sin (pi / 12) * cos (3 pi / 4) - cos (pi / 12) * sin (3 pi / 4)$ ?

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Answer 1 · 2018-06-27T02:57:45

$-sqrt3/2$

Recall

$sin(A-B)=sinAcosB-cosAsinB$

$sin(pi/12)cos((3pi)/4)-cos(pi/12)sin((3pi)/4)=sin(pi/12-(3pi)/4)$

$sin(pi/12-(9pi)/12)$

Recall

$sin(-x)=-sin(x)$

$sin(-(2pi)/3)=-sin((2pi)/3)$

$-sqrt3/2$

How do you evaluate sin (pi / 12) * cos (3 pi / 4) - cos (pi / 12) * sin (3 pi / 4)sin (pi / 12) * cos (3 pi / 4) - cos (pi / 12) * sin (3 pi / 4)?