Verify sin3x = (sins)(3-4sin2x) by algebraic means

Question

Verify sin3x = (sins)(3-4sin²x) by algebraic means 

Answer 1

Assuming the right hand side should be (sin x)(3-4sin^2x)

 

Expanding the left hand side first using sin (A+B) identities

 

sin 3x=sin(2x+x)=sin(2x)cos x+cos(2x)sin x

 

Expand again

 

cos x(2sin x cos x)+sin x(cos²x-sin²x)

 

Factor out sin x

 

sin x(2cos²x+cos²x-sin²x)

 

sin x(3cos²x-sin²x)

 

Use identity sin²x+cos²x=1 to substitute for cos²x

 

sin x(3(1-sin²x)-sin²x)

 

Expand and collect like terms

 

sin x(3-4sin²x)=Right hand side

Answer 2

There's an error on the right side:  sins  ⇐ not meaningful.  Correct this question.