Express the following as a sum of two trigonometric ratios. Sin5xCos3x
Answers
Answer:
sinA+sinB=2sin((A+B)/2)cos((A-B)/2), so sin((A+B)/2)cos((A-B)/2)=1/2(sinA+sinB).
(1/2)(A+B)=5x and (1/2)(A-B)=3x, therefore, adding these two equations: A=8x and subtracting them: B=2x.
Therefore, (1/2)(sin8x+sin2x)=sin5xcos3x
Given : Sin5x . Cos3x
To Find : Express as a sum of two trigonometric ratio
Solution:
Sin C + SinD = 2 Sin (C + D)/2 Cos (C - D)/2
Sin (C + D)/2 Cos (C - D)/2 = Sin5x . Cos3x
(C + D )/2 = 5x
=> C + D = 10x
(C - D)/2 = 3x
=> C - D = 6x
Adding Both 2C = 16x => C = 8x
D = 2x
Sin8x + sin 2x = 2sin5xcos3x
=> sin5xcos3x = (1/2) ( sin8x + sin2x)
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