Answer:
10[tex]sin^{2} ([/tex]β[tex])[/tex]
Step-by-step explanation:
We can find this two ways, first by seeing in the step after it, cosines are canceled out. Since you already have 10[tex]sin^{2} ([/tex]β[tex])[/tex] on the next step, you can assume that (since only the cosines changed and the cosine next ot the blank was removed), the value is 10[tex]sin^{2} ([/tex]β[tex])[/tex].
You can also use double angle formulas from the previous step:
(sin(2β) = 2 sin(β) cos(β))and find that:
5 sin (2β) sin(β) = 5 * (2 sin(β) cos(β)) sin(β)) = (10 sin(β) sin(β)) cos(β) =
10[tex]sin^{2} ([/tex]β[tex])[/tex] cos(β)
But since cos(β) is already present, we can see that the answer is 10[tex]sin^{2} ([/tex]β[tex])[/tex]
