The trigonometric identity 4cos(-5B) sin3B is equivalent to 2[sin(8B) - sin(2B)]
Since we have 4cos(-5B) sin3B
Using the trigonometric identity
sin(x + y) - sin(x - y) = 2cosxsiny
So, cosxsiny = [sin(x + y) - sin(x - y)]/2
Since we have 4cos(-5B) sin3B, comparing cos(-5B) sin3B with cosxsiny, we have
x = -5B and y = 3B
So, we have cos(-5B)sin3B = [sin(-5B + 3B) - sin(-5B - 3B)]/2
= [sin(-2B) - sin(-8B)]/2
= [-sin(2B) - {-sin(8B)}]/2 [since sin(-2B) = -sin(2B)]
= [-sin(2B) + sin(8B)]/2
= [sin(8B) - sin(2B)]/2
So, 4cos(-5B)sin3B = 4 × [sin(8B) - sin(2B)]/2
= 2[sin(8B) - sin(2B)]
So, the trigonometric identity 4cos(-5B) sin3B is equivalent to 2[sin(8B) - sin(2B)]
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