Answer:
2sin2(x). cos( x)
Step-by-step explanation:
As per the trigonometric identities sin3(x)= 3sin(x) - 4sin^3 (x)
putting this in the given expression
sin3x +sinx = 3sin(x) - 4sin^3 (x)+ sinx
= 4sinx - 4sin^3 (x)
= 4sinx(1 - sin^2 (x))
As per the trigonometric identities cos^2(x) = 1-sin^2 (x)
putting this in the above expression
= 4sinxcos^2 (x)
= 2cos(x) (2sin(x)cos(x))
As per the trigonometric identities 2sinx.cosx = sin2(x)
putting this in the above expression
= 2cosx sin2(x)
=2sin2(x). cos( x)
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