How do you express $sin (\frac{π}{12}) \cdot cos (\frac{3 π}{8})$ $sin(pi/12) * cos((3pi)/8 )$ without products of trigonometric functions?

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Answer 1 · 2016-03-24T00:09:14

$sin (\frac{π}{12}) cos (3 \frac{π}{8})$ $\sin(\pi/12)\cos(3\pi/8)$

$= (\frac{1}{2}) (sin (11 \frac{π}{24}) - sin (7 \frac{π}{24}))$ $=(1/2)(\sin(11\pi/24)-\sin(7\pi/24))$

Use these identities to simplify this kind of product:

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

$= (\frac{1}{2}) (cos (a - b) cos (a + b))$ $=(1/2)(\cos(a-b)\cos(a+b))$

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

$= (\frac{1}{2}) (sin (a + b) + sin (a - b))$ $=(1/2)(\sin(a+b)+\sin(a-b))$

$= (\frac{1}{2}) (sin (a + b) - sin (b - a))$ $=(1/2)(\sin(a+b)-\sin(b-a))$

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

$= (\frac{1}{2}) (cos (a + b) + cos (a - b)$ $=(1/2)(\cos(a+b)+\cos(a-b)$

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