<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%28csc%20x%2B1%29%28csc%20x-1%29%7D%7Bcsc%5E2x%7D%5C%5C" id="TexFormula1" title="\fr

All categories

3 years ago

ac{(csc x+1)(csc x-1)}{csc^2x}\\" alt="\frac{(csc x+1)(csc x-1)}{csc^2x}\\" align="absmiddle" class="latex-formula">

cscθ·cos^2θ+sinθ= cscθ

Mathematics

1 answer:

tigry1 [53]3 years ago

7 0

Step-by-step explanation:

$\frac{( \csc x+1)( \csc x-1)}{ \csc ^2x} = \frac{ { \csc }^{2} x - 1}{ \csc^{2} x} \\ = 1 - \sin^{2} x = \cos^{2} x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

b. Since csc theta = 1/sin theta, we can multiply both sides by sin theta and you will end up with

$\cos^{2} \theta + \sin^{2} \theta = 1$

which is an identity.

You might be interested in

Https://allmylinks.com/zeoathiras I’m bored. Owo

Savatey [412]

Answer:

Yeah same here

Step-by-step explanation:

8 0

2 years ago

Solve the following system : -x + 5y = 8 and 3x + 7y = -2

poizon [28]

-x + 5y = 8

multiply this equation by 3

-3x + 15y = 24

now add it to the other equation ( elimination)

-3x + 15y = 24

3x + 7y = -2

-----------------------

0x + 22 y = 22

divide each side by 22

y =1

substitute into -x + 5y =8 to find x

-x + 5(1) = 8

-x + 5 = 8

-x =3

divide by -1

x =-3

Answer (-3,1)

Choice A

4 0

3 years ago

Find the measure of arc RT in the following circle:

Viktor [21]

Answer: look it up bro

Step-by-step explanation:

6 0

2 years ago

Without graphing the equations, decide whether the system has one solution, no solution, or infinitely many solutions.

lbvjy [14]

It has one solution

4 0

2 years ago

The 2008 Workplace Productivity Survey, commissioned by LexisNexis and prepared by World One Research, included the question, "H

LenaWriter [7]

Answer:

A 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

Step-by-step explanation:

We are given that x is normally distributed with a known standard deviation of 12.6.

A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average mean response = 9 hours

$\sigma$ = population standard deviation = 12.6

n = sample of legal professionals = 250

$\mu$ = mean number of hours a legal professional works

Here for constructing a 95% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $9-1.96 \times {\frac{12.6}{\sqrt{250} } }$ , $9+1.96 \times {\frac{12.6}{\sqrt{250} } }$ ]

= [7.44 hours, 10.56 hours]

Therefore, a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

5 0

2 years ago