Question

URGENT! Which of the following correctly expresses sin(2θ)−sin(6θ) as a product?

Select the correct answer below:


2sin(4θ)cos(2θ)

2sin(2θ)cos(4θ)

−2sin(2θ)cos(4θ)

−2sin(2θ)sin(4θ)

Answer 1

−2sin(2θ)cos(4θ)

Explanation:

sin(2∅)-sin(6∅)

Sum product Identity

sinα - sinβ = 2cos((α+β)/2)sin((α-β)/2)

Putting α= 2∅ and β= 6∅ in the identity we get

sin(2∅)-sin(6∅) = 2cos((2∅+6∅)/2)sin((2∅-6∅)/2)

=2cos(8∅/2)sin(-4∅/2)

=2cos(4∅)sin(-2∅)

= -2sin(2∅)cos(4∅)