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Mrrafil [7]
3 years ago
8

Verifying Trig Functions

Mathematics
1 answer:
anzhelika [568]3 years ago
5 0

Answer:

The answer to your question is below

Step-by-step explanation:

                csc α - cot α = \frac{sin \alpha }{1 + cos \alpha }

Work with the left part

                \frac{1}{sin\alpha } - \frac{cos \alpha }{sin \alpha}

Simplify

                \frac{1 - cos\alpha }{sin\alpha }

Multiply by the reciprocal

 \frac{1 - cos\alpha }{sin \alpha } x \frac{1 + cos\alpha }{1 + cos\alpha }                                  

Simplify

\frac{1 - cos^{2}\alpha}{sin\alpha (1 + cos\alpha)}

Remember that

                 sin²α = 1 -cos²α

Substitute the previous equation

\frac{sin^{2}\alpha }{sin\alpha(1 + cos\alpha ) }

Simplify

\frac{sin\alpha}{1 + cos \alpha}      

The identity i proved.            

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A car moves at 45 miles per hour. The time and the distance it travels are recorded.
irinina [24]

Answer:

the distance

Step-by-step explanation:

More time care travels, more distance it goes. So distance depends of the time.

4 0
3 years ago
How much water should be added to 3 gallons of pure acid in order to obtain the 15% acid solution? HELP DUE BY TOMMOROW MORNING
Pani-rosa [81]
3 gallons of acid = 100% concentration acid
? (water+acid) gallons = 15 concentration acid

Note: Every gallon of water added reduces the percentage concentration of acid. Therefore, the relationship is inverse proportionality.

Solution:

Total number of gallons (water+acid) = (3*100)/15 = 20 gallons
Therefore, gallons of water = 20-3 = 17 gallons
5 0
3 years ago
How to solve x/-3-2=5.5
amid [387]
Okay first set up the equation

 x
---      -2     = 5.5
-3

add over the 2

 x
---  = 7.5
-3

now you need to multiply the denominator by the answer

(-3)(7.5) = x
-22.5 = x
3 0
3 years ago
Marty made a $220 bank deposit using $10 bills and $5 bills. She gave the teller a total of 38 bills, how many $5 bills were in
Luda [366]

ANSWER: 32 five-dollar bills

======

EXPLANATION:

Let x be number of $5 bills

Let y be number of $10 bills

Since we have total of 38 bills, we must have the sum of x and y be 38

x + y = 38 (I)

Since the total amount deposited is $220, we must have the sum of 5x and 10y be 220 (x and y are just the "number of" their respective bills, so we multiply them by their value to get the total value):

5x + 10y = 220 (II)

System of equations:

\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ 5x + 10y &= 220 && \text{(II)} \end{aligned} \right.

Divide both sides of equation (II) by 5 so our numbers become smaller

\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ x + 2y &= 44 && \text{(II)} \end{aligned} \right.

Rearrange (I) to solve for y so that we can substitute into (II)

\begin{aligned} x + y &= 38 && \text{(I)} \\ y &= 38 - x \end{aligned}

Substituting this into equation (II) for the y:

\begin{aligned} x + 2y &= 44 && \text{(II)} \\ x + 2(38 - x) &= 44\\ x + 76 - 2x &= 44 \\ -x &= -32 \\ x &= 32 \end{aligned}

We have 32 five-dollar bills

======

If we want to finish off the question, use y = 38 - x to figure out number of $10 bills

y = 38 - 32 = 6

32 five-dollar bills and 6 ten-dollar bills

7 0
3 years ago
Draw a net for each of the following shapes:
Margarita [4]
A. You would start off by a rectangle in the middle, then you would place to squares on the bottom and top if the rectangle. After you've done that, you place two rectangles (Same size as the original) on both sides of the original rectangle. Finally you add a rectangle (Same size) to either ends of the secondary rectangles. It should look like this.


B. You would start off with a rectangle in the middle, then you would add 2 equilateral triangles to the top and bottom of the rectangle. After that, you Simply put 2 rectangles (Same size as the original) on both sides of the rectangle. It should look something like this.

C. To make a pyramid, it's actually quite simple. You would start off with a square in the middle, and then place equilateral triangles on ALL sides of the square. It should look something like this.

I hope this helped ^^

4 0
3 years ago
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