convert the following sum into product
sin 4x + cos 2x
Answers
Given : sin 4x + cos 2x
To Find : convert the sum into product
Solution:
sin 4x + cos 2x
sin ( π/2 - A) = cosA
= sin 4x + sin ( π/2 - 2x)
SinC + sin D = 2 Sin{ ( C + D)/2} Cos {(C - D) /2}
= 2 Sin ( 4x + π/2 - 2x)/2 Cos ( 4x - π/2 + 2x)/2
= 2 Sin ( x + π/4) Cos ( 3x - π/4)
sin 4x + cos 2x = 2 Sin ( x + π/4) Cos ( 3x - π/4)
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