How do you express $cos (\frac{π}{4}) \cdot sin (\frac{13 π}{8})$ $cos(pi/ 4 ) * sin( ( 13 pi) / 8 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{π}{4}) \cdot sin (\frac{13 π}{8})$ $cos(pi/ 4 ) * sin( ( 13 pi) / 8 )$ without using products of trigonometric functions?

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Answer 1 · 2016-04-12T11:42:59

$\frac{sin (\frac{15 π}{16}) + sin (\frac{11 π}{16})}{2}$ $(sin((15pi)/16)+sin((11pi)/16))/2$

Explanation:

Use $sin (A + B) cos (A - B) = \frac{sin 2 A + sin 2 B}{2} =$ $sin (A+B)cos(A-B)=(sin 2A + sin 2B)/2 =$
Here, $A + B = 13 \frac{π}{8} and A - B = \frac{π}{4}$ $A+B=13pi/8 and A-B=pi/4$
Add and subtract.
$2 A = 15 \frac{π}{8} . A + 15 \frac{π}{16} . 2 B = 11 \frac{π}{8} . B = 11 \frac{π}{16}$ $2A = 15pi/8. A + 15pi/16. 2B = 11pi/8. B = 11pi/16$ .
Answer: $\frac{sin (\frac{15 π}{16}) + sin (\frac{11 π}{16})}{2}$ $(sin((15pi)/16)+sin((11pi)/16))/2$

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How do you express $cos (\frac{π}{4}) \cdot sin (\frac{13 π}{8})$ $cos(pi/ 4 ) * sin( ( 13 pi) / 8 )$ without using products of trigonometric functions?

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Explanation:

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How do you express $cos (\frac{π}{4}) \cdot sin (\frac{13 π}{8})$ $cos(pi/ 4 ) * sin( ( 13 pi) / 8 )$ without using products of trigonometric functions?