I will use the letter x instead of theta.
Then the problem is, given sec(x) + tan(x) = P, show that
sin(x) = [P^2 - 1] / [P^2 + 1]
I am going to take a non regular path.
First, develop a little the left side of the first equation:
sec(x) + tan(x) = 1 / cos(x) + sin(x) / cos(x) = [1 + sin(x)] / cos(x)
and that is equal to P.
Second, develop the rigth side of the second equation:
[p^2 - 1] / [p^2 + 1] =
= [ { [1 + sin(x)] / cos(x) }^2 - 1] / [ { [1 + sin(x)] / cos(x)}^2 +1 ] =
= { [1 + sin(x)]^2 - [cos(x)]^2 } / { [1 + sin(x)]^2 + [cos(x)]^2 } =
= {1 + 2sin(x) + [sin(x)^2] - [cos(x)^2] } / {1 + 2sin(x) + [sin(x)^2] + [cos(x)^2] }
= {2sin(x) + [sin(x)]^2 + [sin(x)]^2 } / { 1 + 2 sin(x) + 1} =
= {2sin(x) + 2 [sin(x)]^2 } / {2 + 2sin(x)} = {2sin(x) ( 1 + sin(x)} / {2(1+sin(x)} =
= sin(x)
Then, working with the first equation, we have proved that [p^2 - 1] / [p^2 + 1] = sin(x), the second equation.
If log a^2/82819 then the value of x is 021819201010
Answer:
Area: 168
Step-by-step explanation:
Area equals base times height. B= 14 and H= 12 so 14 × 12= 168
Answer:
421
Step-by-step explanation:
Margin of error = E = 0.04
Confidence Level = 90%
z value associated with this confidence level = z = 1.645
Previous estimate of population proportion = p = 0.54
q = 1 - p = 1 - 0.54 = 0.46
The formula of Margin of Error for population proportion is:
Here, n is the sample size.
Re-arranging the equation for n and using the values we get:
Thus the minimum sample size required to estimate the proportion of adults who have high speed internet access is 421
Answer:
y = 2x + 14
Step-by-step explanation:
Equation in slope intercept form:
y = mx + c
From the scenario above ;
y = total miles = 30
Average mile gain per week = slope (m) = 2
Number of weeks (x) = 8
We can obtain intercept, c :
30 = 2(8) + c
30 = 16 + c
30 - 16 = c
14 = c
Hence,
Equation goes thus ;
y = 2x + 14
