Answer:
20%
10%
0.5
5%
Step-by-step explanation:
Price elasticity of demand measures the responsiveness of quantity demanded to changes in price of the good.
Price elasticity of demand = percentage change in quantity demanded / percentage change in price
Percentage change in price = (1.2/1) - 1 = 20%
Percentage change in quantity demanded = 450/500 - 1 = 10%
Given:
<span>tan(B/2) = sec(B) / (sec(B) * csc(B) + csc(B)) </span>
<span>Apply the half angle formula to convert tan(B/2) to terms of B: </span>
<span>sin(B) / (1+cos(B)) = sec(B) / (sec(B) * csc(B) + csc(B)) </span>
<span>Convert everything else to be in terms of sin and cos: </span>
<span>sin(B) / (1+cos(B) = (1/cos(B)) / ((1/cos(B)) * (1/sin(B)) + (1/sin(B))) </span>
<span>Multiply right side by "sin(B)/sin(B)" to simplify the fractions: </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1/cos(B)) + 1) </span>
<span>Change "1" to cos(B)/cos(B) and then combine over </span>
<span>common denominator: </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1/cos(B)) + cos(B)/cos(B)) </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1+cos(B))/cos(B)) </span>
<span>Dividing by a fraction equals multiplying by its reciprocal: </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) * (cos(B) / (1+cos(B))) </span>
<span>Multiply terms on the right side (canceling cos(B) terms): </span>
<span>sin(B) / (1+cos(B) = sin(B) / (1+cos(B)) </span>
Given:
The expression is
To find:
The expression which is equivalent to the given expression.
Solution:
We have,
We know that,
Using this formula, the given expression can be written as
Therefore, the given expression is equivalent to 1.
