Answer:
-15
Step-by-step explanation:
We proceed as follows;
In this question, we want to fill in the blank so that we can have the resulting expression expressed as the product of two different linear expressions.
Now, what to do here is that, when we factor the first two expressions, we need the same kind of expression to be present in the second bracket.
Thus, we have;
2a(b-3) + 5b + _
Now, putting -15 will give us the same expression in the first bracket and this gives us the following;
2a(b-3) + 5b-15
2a(b-3) + 5(b-3)
So we can have ; (2a+5)(b-3)
Hence the constant used is -15
Answer:
The blue dot represents the absolute value of the number occupied by red dot.
The first step to solving this is to use tan(t) =

to transform this expression.
cos(x) ×

Using cot(t) =

,, transform the expression again.
cos(x) ×

Next you need to write all numerators above the least common denominator (cos(x)sin(x)).
cos(x) ×

Using sin(t)² + cos(t)² = 1,, simplify the expression.
cos(x) ×

Reduce the expression with cos(x).

Lastly,, use

= csc(t) to transform the expression and find your final answer.
csc(x)
This means that the final answer to this expression is csc(x).
Let me know if you have any further questions.
:)