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)

−2sin(2θ)cos(4θ)

Step-by-step 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∅)

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d