How do you express sin(pi/12) * cos((3pi)/8 ) sin(π12)cos(3π8) without products of trigonometric functions?

1 Answer
Mar 24, 2016

\sin(\pi/12)\cos(3\pi/8)sin(π12)cos(3π8)

=(1/2)(\sin(11\pi/24)-\sin(7\pi/24))=(12)(sin(11π24)sin(7π24))

Explanation:

Use these identities to simplify this kind of product:

\sin(a)\sin(b)sin(a)sin(b)

=(1/2)(\cos(a-b)\cos(a+b))=(12)(cos(ab)cos(a+b))

\sin(a)\cos(b)sin(a)cos(b)

=(1/2)(\sin(a+b)+\sin(a-b))=(12)(sin(a+b)+sin(ab))

=(1/2)(\sin(a+b)-\sin(b-a))=(12)(sin(a+b)sin(ba))

\cos(a)\cos(b)cos(a)cos(b)

=(1/2)(\cos(a+b)+\cos(a-b)=(12)(cos(a+b)+cos(ab)