How do you simplify this expression step by step?

Answers

Answer 1

Answer:

$\bf \textit{Pythagorean Identities} \n\n sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \n\n[-0.35em] \rule{34em}{0.25pt}\n\n \cfrac{csc(\theta )-sin(\theta )}{cos(\theta )}\implies \cfrac{~~(1)/(sin(\theta ))-sin(\theta )~~}{cos(\theta )}\implies \cfrac{~~(1-sin^2(\theta ))/(sin(\theta ))~~}{cos(\theta )}$

$\bf \cfrac{1-sin^2(\theta )}{sin(\theta )}\cdot \cfrac{1}{cos(\theta )}\implies \cfrac{\stackrel{cos(\theta )}{\begin{matrix} cos^2(\theta ) \n[-0.7em]\cline{1-1}\n[-5pt]\end{matrix}} }{sin(\theta )}\cdot \cfrac{1}{\begin{matrix} cos(\theta ) \n[-0.7em]\cline{1-1}\n[-5pt]\end{matrix} }\implies \cfrac{cos(\theta )}{sin(\theta )}\implies cot(\theta )$

Answer 2

Answer:

Answer:

cot Ф

Step-by-step explanation:

Recall that sin²Ф + cos²Ф = 1, (which also says that cos²Ф - 1 = sin²Ф).

Also recall the definitions of the csc, sin and cos functions.

Your expression is equivalent to:

1 sin Ф

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

sin Ф 1

===================

cos Ф

There are three terms in your expression: csc, sin and cos. Multiply all of them by sin Ф. The result should be:

1 - sin²Ф

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

sin Ф · cos Ф

Using the Pythagorean identity (see above), this simplifies to

cos²Ф

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

sin Ф·cos Ф

and this whole fraction reduces to

cos Ф

-------------- and this ratio is the definition of the cot function.

sin Ф

Thus, the original expression is equivalent to cot Ф

Related Questions

NEED HELP WITH MATH! Will Give brainliest!
On the first day of the fiscal year, a company issues $65,000, 6%, five-year installmentnotes that have annual payments of $15,431. The first note payment consists of $3,900 ofinterest and $11,531 of principal repayment.a. Journalize the entry to record the issuance of the installment notes.b. Journalize the first annual note payment.
Give B (-4,-6) under which selection is B'(4,6)?
A 13 ft ladder is resting on a wall. The angle the ladder makes with the floor is 45 degrees. How high off the ground is the top of the ladder?Use the function y=13cos(theta) to find the answer
Determine the measure of < 7o 53o 133o 127o 47

For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hour and δ=4 miles per hour. Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

Answers

Answer:

$Z = 1$

Step-by-step explanation:

Z - score

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 61, \sigma = 4$

Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

This is Z when X = 65. So

$Z = (X - \mu)/(\sigma)$

$Z = (65 - 61)/(4)$

$Z = 1$

A box contains 5 plain pencils and 5 pens. A second box contains 3 color pencils and 7 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected

Answers

The events 'select a plain pencil' and 'select a color pencil' are independent. therefore the probability of both occurring is the product of their probabilities:
$P(plain\ pencil\ and\ color\ pencil)=(5)/(10)*(3)/(10)=(3)/(20)$
The answer is 3/20 or 0.15.

A culture started with 5000 bacteria after three hours it grew 6500 bacteria predict how many bacteria will be present after 13 hours round your answer to the nearest whole number

Answers

Answer:

15595 bacteria will be present after 13 hours.

Step-by-step explanation:

Continuous population growth:

The continuous population growth model, for the population after t hours, is given by:

$P(t) = P(0)e^(rt)$

In which P(0) is the initial population and r is the growth rate.

Started with 5000 bacteria

This means that $P(0) = 5000$

$P(t) = 5000e^(rt)$

After three hours it grew 6500 bacteria:

This means that $P(3) = 6500$ . We use this to find r.

$P(t) = 5000e^(rt)$

$6500 = 5000e^(3r)$

$e^(3r) = (65)/(50)$

$\ln{e^(3r)} = \ln{(65)/(50)}$

$3r = \ln{(65)/(50)}$

$r = \frac{\ln{(65)/(50)}}{3}$

$r = 0.0875$

$P(t) = 5000e^(0.0875t)$

How many bacteria will be present after 13 hours?

This is P(13). So

$P(13) = 5000e^(0.0875*13) = 15594.8$

Rounding to the nearest whole number

15595 bacteria will be present after 13 hours.

If the triangles are congruent,then x = [?]
13
4x+1
2x+y
8x-2y
Enter the number that belongs in
the green box
Enter

Answers

Answer:

x = 3

Step-by-step explanation:

If the triangles are congruent then

4x + 1 = 13

4x = 12

x = 3

Can someone please help? U get points just from typing and I would really appreciate it.The sum of two consecutive numbers is 131. What are the two numbers?
A. 64 and 65
B. 64 and 67
C. 65 and 66
D. 130 and 131

No links or fake answers pls. Thank you for understanding.

Answers

Answer:

Step-by-step explanation:

Consecutive numbers are directly next to each other on the number line, so B is already out of the question. Add each pair together to see which one is 131.

Answer:

C. 65 and 66

Step-by-step explanation:

Let x be first number

Then x + 1 be next number

x + (x + 1) = 131

2x + 1 = 131

2x = 130

x = 65

x + 1 = 66

Which Polygons are similar to A? PLEASE ANSWER QUICKLY