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OLEGan [10]
3 years ago
6

Verify the identity. Please show your work.

Mathematics
1 answer:
m_a_m_a [10]3 years ago
5 0

Step-by-step explanation:

To prove :

( 1 - sin x ) ( 1 + sin x ) = sec² x

LHS : -

( 1 - sin x ) ( 1 + sin x )

Formula / Identity : -

( a - b ) ( a + b ) = a² - b²

Here,

a = 1

b = sin x

( 1 - sin x ) ( 1 + sin x )

= 1 - sin² x

Identify : -

sin² θ + cos² θ = 1

cos² θ = 1 - sin² θ

Similarly,

1 - sin² x

= cos² x

= RHS

Hence verified.

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Consider g (x) = StartFraction 4 x + 9 Over x Superscript 6 Baseline + 1 EndFraction Which statement correctly uses limits to de
Nastasia [14]

To find the end behavior of a function, we find it's limits as x approaches infinity, getting the correct option as:

As x approaches plus-or-minus infinity = limit of StartFraction 4 Over x Superscript 5 EndFraction as x approaches plus-or-minus infinity, so as x approaches infinity, g (x) approaches 0.

Function:

The function given is:

g(x) = \frac{4x+9}{x^6+1}

Limit as x goes to infinity:

To find the limit of a function as x goes to infinity, we consider the term with the highest exponent in the numerator and in the denominator. So

\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{4x+9}{x^6+1} = \lim_{x \rightarrow \infty} \frac{4x}{x^6} = \lim_{x \rightarrow \infty} \frac{4}{x^5} = \frac{4}{\infty^5} = 0

The graphic of the function, given at the end of this answer, corroborates the answer.

Thus, the correct option is:

As x approaches plus-or-minus infinity = limit of StartFraction 4 Over x Superscript 5 EndFraction as x approaches plus-or-minus infinity, so as x approaches infinity, g (x) approaches 0.

For more on limits as x approaches infinity, you can check brainly.com/question/12207599.

7 0
3 years ago
Read 2 more answers
Why might two people in the same state with the same salary pay different rates of income tax?
vekshin1

One <em><u>possible answer</u></em> is:

They could have had extra money withheld when they completed their W-4.

Explanation:

When you complete the W-4, there is a worksheet that you fill out to help you decide what number of exemptions to claim. However, you can choose to have more money withheld, to ensure you have no tax obligations at the end of the year. This would cause the amount of money withheld from two different people to potentially be different.

3 0
4 years ago
How do you convert decimals between standard and expanded form
nordsb [41]

Answer:

Heres how:

Step-by-step explanation:

Example, 7.831 , here you can see that there are 3 numbers relating to a decimal. the 1 by itself is 0.1000, 3 by itself is 0.300, and the 8 by itself is 0.80 . If you add this, you get 0.831. now add the whole number, Seven. if there is more digits in the decimal, then just add another zero.

7 0
3 years ago
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Which of the following is the measure of side a?<br> 23.3<br> 144<br> 8<br> 16
jenyasd209 [6]

Step-by-step explanation:

it is a right-angled triangle, so the side lengths need to fulfill the Pythagoras rule :

c² = a² + b²

where c is the Hypotenuse, the baseline opposite of the 90 degree angle. and a and b (often called legs) are the sides "enclosing" the 90 degree angle.

so, we have

20² = a² + 12²

400 = a² + 144

a² = 256

a = 16

FYI - we could have picked the right answer also by eliminating the wrong given answer options.

as this is a right-angled triangle :

a cannot be longer than the baseline (20).

that eliminates already the first 2 options.

and then look at the picture : a cannot be shorter than b (the other side line (12)).

that eliminates the third option.

4 0
3 years ago
Do students learn algebra 2 better from an online course or in class with a teacher? to find out, a large high school set up an
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Answer:

b) using technology

Step-by-step explanation:

4 0
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