How do you express cos(pi/ 4 ) * sin( ( 13 pi) / 8 ) cos(π4)sin(13π8) without using products of trigonometric functions?

1 Answer
Apr 12, 2016

(sin((15pi)/16)+sin((11pi)/16))/2sin(15π16)+sin(11π16)2

Explanation:

Use sin (A+B)cos(A-B)=(sin 2A + sin 2B)/2 =sin(A+B)cos(AB)=sin2A+sin2B2=
Here, A+B=13pi/8 and A-B=pi/4A+B=13π8andAB=π4
Add and subtract.
2A = 15pi/8. A + 15pi/16. 2B = 11pi/8. B = 11pi/162A=15π8.A+15π16.2B=11π8.B=11π16.
Answer: (sin((15pi)/16)+sin((11pi)/16))/2sin(15π16)+sin(11π16)2