Express as a product: 4sin^2(a-3)

Answer 1

4sin²(a-3) = 4(1 - cos²(a-3)) = 4(1 - cos(a-3))(1 + cos(a-3))

Answer 2

4(sin^2(a-3))=

(2sin(a-3))(2sin(a-3))

= 2(sinacos3-sin3cosa)(2)(sinacos3-sin3cosa)

use the sum formula for sines

sin(A+B)=sinAcosB+sinBcosA

or difference formula for sines

sin(A-B) = sinAcosB-sinBcosA

with A=a and B=3