Please study the graph and select all the true statements.

Show that √(1-cos A/1+cos A) =cosec A - cot A

Gennadij [26K]

Hi there!

$\sqrt{\frac{1-cosA}{1+cosA}} =$

We can begin by multiplying by its conjugate:

$\sqrt{\frac{1-cosA}{1+cosA}} * \sqrt{\frac{1+cosA}{1+cosA}} = \\\\\sqrt{\frac{(1-cosA)(1 + cosA)}{(1+cosA)(1 + cosA)}} =$

Simplify using the identity:

$1 - cos^2A = sin^2A$

$\sqrt{\frac{(1-cos^2A)}{(1+cosA)^2}} =\\\\\sqrt{\frac{(sin^2A)}{(1+cosA)^2}} =$

Take the square root of the expression:

${\frac{sinA}{1+cosA} =$

Multiply again by the conjugate to get a SINGLE term in the denominator:

${\frac{sinA}{1+cosA} * {\frac{1-cosA}{1-cosA} =\\$

Simplify:

${\frac{sinA(1-cosA)}{1-cos^2A} =$

Use the above trig identity one more:

${\frac{sinA(1-cosA)}{sin^2A} =$

Cancel out sinA:

${\frac{(1-cosA)}{sinA} =$

Split the fraction into two:

${\frac{1}{sinA} - \frac{cosA}{sinA} =$

Recall:

$1/sinA = cscA\\\\cosA/sinA = cotA$

Simplify:

$\frac{1}{sinA} + \frac{cosA}{sinA} = \boxed{cscA - cotA}$

5 0

2 years ago

What is the solution to f(x)=8^5/3

11111nata11111 [884]

Answer:

13.3f

Step-by-step explanation:

5 0

3 years ago

You and your friend each collect rocks and fessis your friend collects three times as many roots and half as many fossils as you

n200080 [17]

Answer:

Number of rocks and fossils collected by you is 1 and 24 respectively

Number of rocks and fossils collected by your friend is 3 and 12 respectively

Step-by-step explanation:

Let the number of Rocks you collect be x

Let the number of Fossils you collect be y

Then the total number pf objects you collected will be

x + y = 25

x = 25 - y------------------------------(1)

Your friend collects three times as many rocks and half as many fossils as you.

This can be written as

3x + y (1/2) = 15

3x + (y/2) = 15-------------------(2)

Substituting (1) in (2)

3(25 - y) + (y/2) = 15

75 - 3y + (y/2) = 15

Grouping the like terms we get,

75 - 15 = 3y = (y/2)

60 = ( 6y - y /2)

60 x 2 = 6y -y

120 = 5y

y = 120/5

y = 24

Substituting y value in equation(1) we get

x = 25 - 24

x= 1

y= 24

Friends collects 3 times rock

so collects 3x =3(1) = 3rocks

Also he collects half as many fossils

That is

y/2 = 24/2 = 12 fossils

Hope this help you! :)

5 0

3 years ago

WANT POINTS JUST ANSWER THIS CORRECTLY FOR 45!!!

Lelu [443]

Since we’re trying to find minutes, concert all known information to minutes

1 hr 15 mins = 75 mins
1 hr 30 mins = 90 mins

Next, calculate how many total minutes Gage has skated in the first 8 days

75(5) + 90(3) = 645 mins

Create an equation to find the average of Gage’s minutes of skating. Add up all the minutes and divide by the total amount of days and set equal to 85, the average we are trying to get.

(645 mins + x mins)/9 days = 85

Solve for x

645 + x = 765
x = 120

So, in order to have an average of an 85 minute skate time, Gage would need to skate 120 minutes on the ninth day.

3 0

3 years ago

What are the x and y-intercepts of the line described by the equation?

KiRa [710]

Answer:

x-int (6.2, 0)

y-int (0, 3.1)

Step-by-step explanation:

x-intercept is found when y = 0.

y-intercept is found when x = 0.

Step 1: Define equation

2x + 4y = 12.4

Step 2: Find x-intercept

Substitute y for 0.

2x + 4(0) = 12.4

2x = 12.4

x = 6.2

(6.2, 0)

Step 3: Find y-intercept

Substitute x for 0.

2(0) + 4y = 12.4

4y = 12.4

y = 3.1

(0, 3.1)

6 0

3 years ago