Question

HELP!! I'm not sure what goes in the blank.

Answer 1

Answer:

10$sin^{2} ($β$)$

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$sin^{2} ($β$)$ 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$sin^{2} ($β$)$.

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$sin^{2} ($β$)$ cos(β)

But since cos(β) is already present, we can see that the answer is 10$sin^{2} ($β$)$