The expression equivalent to sin 3x + sin x is .

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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the answer will be the last one