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stiks02 [169]
3 years ago
5

Simplify the expression 1/√(1-cos^2 x) . Remember cos x= 1/csc x

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
3 0
First, we are going to use the Pythagorean identity: sin^2(x)+cos^2(x)=1 to rewrite our expression. Solving for sin^2(x) in our Pythagorean identity  we get that sin^2(x)=1-cos^2(x), so we can rewrite our expression as follows:
\frac{1}{ \sqrt{1-cos^2(x)} } = \frac{1}{ \sqrt{sin^2(x)} } = \frac{1}{sin(x)}

Next, we are going to use the trig identity: csc(x)= \frac{1}{sin(x)} to completely simplify our expression:
\frac{1}{sin(x)} =csc(x)

We can conclude that \frac{1}{ \sqrt{1-cos^2(x)} }=csc(x)
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Which of the following are examples of a geometric sequence? Select any and all that apply: may be more than one correct answer.
nevsk [136]

Answer:

( 1 , -2 , 4 , -8 , 16 , ... )

( 9 , 3 , 1 , 1/3 , 1/9 , ... )

Step-by-step explanation:

A geometric sequence has a common ratio in consecutive terms,

In sequence,

1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....

\frac{1/2}{1}\neq \frac{1/6}{1/2}\neq \frac{1/24}{1/6}\neq \frac{1/120}{1/24}...

i.e.

1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}..... is not a Geometric sequence,

1 , -2 , 3 , -4 , 5 , ...

\frac{-2}{1}\neq \frac{3}{-2}\neq \frac{-4}{3}\neq \frac{5}{-4}...

i.e. 1 , -2 , 3 , -4 , 5 , ... is not a Geometric sequence,

In sequence,

1 , -2 , 4 , -8 , 16 , ...

\frac{-2}{1}=\frac{4}{-2}= \frac{-8}{4}= \frac{16}{-8}...

i.e. 1 , -2 , 4 , -8 , 16 , .... is a Geometric sequence,

In sequence,

0 , 1 , 0 , -1 , 0 , .....

\frac{1}{0}\neq \frac{0}{1}\neq \frac{-1}{0}\neq \frac{0}{-1}...

i.e. 0 , 1 , 0 , -1 , 0 , .....is not a Geometric sequence,

In sequence,

9 , 3 , 1 , 1/3 , 1/9 , ...

\frac{3}{9}=\frac{1}{3}= \frac{1/3}{1}= \frac{1/9}{1/3}...

i.e.  9 , 3 , 1 , 1/3 , 1/9 , ... is a Geometric sequence,

In sequence,

1 , 3 , 5 , 7 , 9 , ...

\frac{3}{1}\neq \frac{5}{3}\neq \frac{7}{5}\neq \frac{9}{7}...

i.e. 1 , 3 , 5 , 7 , 9 , ... is not a Geometric sequence

4 0
3 years ago
F(x) = 9x + 3<br>g(x) = 3x + 1<br>Find:<br>(f/g)(x)​
igomit [66]

Answer:

<h2>(f/g)(x) = 3</h2>

Step-by-step explanation:

f(x) = 9x + 3

g(x) = 3x + 1

To find (f/g)(x) divide f(x) by g(x)

That's

(f/g)(x) =  \frac{9x + 3}{3x + 1}

Factorize f(x)

f(x) = 9x + 3 = 3(3x + 1)

So we have

(f/g)(x) =  \frac{3(3x + 1)}{3x + 1}

Simplify

We have the final answer as

<h3>(f/g)(x) = 3</h3>

Hope this helps you

4 0
3 years ago
Find two consecutive integers such that four times the larger exceeds three times the smaller by 23
Bad White [126]
CONSECUTIVE NUMBERS; x, x+1
(x+1)4=3(x)+23
4x+4=3x+23
4x-3x=23-4
x=19
x+1=20
THEREFORE  the consecutive numbers are 19&20
3 0
3 years ago
Please i need this asap.
yKpoI14uk [10]

<u>Answer (1):</u>

Coefficient of any term  means the number multiplied in that term including sign.

ab^2 is same as 1ab^2.

Hence required coefficient is 1.



<u>Answer (2):</u>

4(3-7)^2+102


=4(-4)^2+102


=4(16)+102


=64+102


=166


Hence final answer is 166


<u>Answer (3):</u>

\sqrt{\frac{49}{25}}


=\frac{\sqrt{49}}{\sqrt{25}}


=\frac{7}{5}


Hence final answer is \frac{7}{5}


4 0
3 years ago
Read 2 more answers
Use the data from the table to create a scatter plot. plot al the data points from the table.
aleksley [76]

Answer:

Place a point at

8,4

5,7

6,5

10,4

2,11

4,7

3,9

1,13

1,11

3,12

4,2

7,2

5,24

9,3

5,5

Step-by-step explanation:

5 0
3 years ago
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