How do you express $sin (\frac{π}{4}) \cdot sin (\frac{π}{12})$ $sin(pi/ 4 ) * sin( ( pi) / 12 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{π}{12})$ $sin(pi/ 4 ) * sin( ( pi) / 12 )$ without using products of trigonometric functions?

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Answer 1 · 2016-03-07T02:11:35

$sinAsinB=-1/2 [cos(A+B)-cos(A-B)] =-> sin (pi/4)sin(pi/12)=-1/2[cos(pi/4 + pi/12)- cos(pi/4-pi/12)]=-1/2[cos(pi/3)-cos(pi/6)]=-1/2[1/2 -sqrt3/2]=-1/4+sqrt3/4=(sqrt3 -1)/4$

Explanation:

Use the sum and product formula and substitute in $pi/4$ for A and $pi/12$ for B then simplify as shown above.

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{π}{12})$ $sin(pi/ 4 ) * sin( ( pi) / 12 )$ without using products of trigonometric functions?

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How do you express sin(pi/ 4 ) * sin( ( pi) / 12 ) sin(π4)⋅sin(π12)sin(pi/ 4 ) * sin( ( pi) / 12 ) without using products of trigonometric functions?

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{π}{12})$ $sin(pi/ 4 ) * sin( ( pi) / 12 )$ without using products of trigonometric functions?