All categories

3 years ago

Verify identities Will give BRAINLIST do not give me trash!!

Mathematics

1 answer:

lilavasa [31]3 years ago

8 0

Answer:

See proof below

Step-by-step explanation

cot^2(x) - csc^2(x) = -1

In trigonometry identity

cot^2x = cos²x/sin²x

Csc²x = 1/sin²x

Substitute into the original expression

cos²x/sin²x - 1/sin²x

Find the LCM

(Cos²x-1)/sin²x .... *

Recall that sin²x+cos²x = 1

Sin²x = 1-cos²x

-sin²x = -1+cos²x

-sin²x = cos²x-1 .... **

Substitute ** into *

(Cos²x-1)/sin²x

-sin²x/sin²x

= -1 (RHS)

Therefore cot^2(x) - csc^2(x) = -1 (Proved!)

You might be interested in

5x+2x=2x+5x is an example of which algebraic property?

Travka [436]

The answer to your question is c.

5 0

3 years ago

If the ordered pair (-5/2,y) lies on the graph of y=7-2x, find the value of y

aev [14]

Y=7-2×(-5/2)
Y=7+5
Y=12
The answer is C

6 0

4 years ago

Read 2 more answers

What is the value of x

LenKa [72]

Answer: x= 98°

Step-by-step explanation:

Concept:

Here, we need to know the concept of the "Exterior Angle theorem"

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite angles of the triangle.

If you are still confused, you may refer to the attachment below for a graphical explanation.

Solve:

x = 53 + 45 = 98°

Hope this helps!! :)

Please let me know if you have any questions

7 0

3 years ago

To estimate the mean height μ of male students on your campus,you will measure an SRS of students. You know from government data

nexus9112 [7]

Answer:

a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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

$Z = \frac{X - \mu}{\sigma}$

This Zscore is how many standard deviations the value of the measure X 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.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

$Z = \frac{X - \mu}{\sigma}$

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$