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.
Answer:
I got 5 for you, the answer is x+4=10 or x+2=10, that's the error. You don't seperate them in parenthises like that, you have to multiply them together. This means it has to be x+4 times x+2. I'll try the others too, but no guarantess here.
If you have a piece of material of a total length of 3 meters and each piece to be cut must be 1 meter then you will only be able to cut 3 pieces.
Hope this helps :)
Answer:
<h2>Revenue will decrease</h2>
Step-by-step explanation:
Note: the question did not provide the quantity to work with, so we will assume some values, say quantity Q= 30
Generally, it is normal for the revenue to decrease when the price of a commodity increase, this is so that buyer will have to react to adjust to the change in price.
When price increase from $50 to $60, the total revenue will decrease
let say the quantity Q1=30 , and the new quantity after price increase is Q2=20
1. The revenue PxQ before price change will be
PxQ= P1xQ1=50*30
PxQ= $1500
1. The revenue PxQ after price change will be
PxQ=P2xQ2= 60*20
P2xQ2= $1200
This clearly shows that based on the assumed data, the total revenue will drop from1500 to 1200, a total of $300 in a decrease
Answer:
false
Step-by-step explanation:
first two angles that aren't the hypotenuse have to be longer than the hl
