Verify that 1 + cot2 x = csc2 x is an identity.

1 answer:

4 0

$\sin ^{ 2 }{ x } +\cos ^{ 2 }{ x } =1\\ \\ \frac { \sin ^{ 2 }{ x+\cos ^{ 2 }{ x } } }{ \sin ^{ 2 }{ x } } =\frac { 1 }{ \sin ^{ 2 }{ x } }$

$\\ \\ \frac { \sin ^{ 2 }{ x } }{ \sin ^{ 2 }{ x } } +\frac { \cos ^{ 2 }{ x } }{ \sin ^{ 2 }{ x } } =\frac { 1 }{ \sin ^{ 2 }{ x } } \\ \\ 1+\cot ^{ 2 }{ x } =\csc ^{ 2 }{ x }$

You might be interested in

Suppose the dial on the spinner is spun 2 times in a row.

Ivenika [448]

The probability of one success and one failure will be 4/9. Table C represents the probability distribution for the variable X.

<h3>What is probability?</h3>

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

The dials on the spinner are spun 2 times in a row.

P(dial lands on region)=P(success) = 2/3

P(failure) = 1/3

The probability that the two times dials on the spinner are not spun 2 times in a row.

P = (1/3)² = 1/9

The probability that the two times dials on the spinner are spun 2 times in a row.

P = (2/3)²= 4/9

One may calculate the probability of one success and one failure using the binomial distribution or by simply deducting the probabilities we previously determined from 1.

P = 1 - 1/9 - 4/9

P = 4/9

The probability of one success and one failure will be 4/9.

Hence table C represents the probability distribution for the variable

To learn more about the probability, refer to the link;

brainly.com/question/11234923

#SPJ1

3 0

2 years ago

Ford and GM pick up trucks are being tested for fuel efficiency, which is commonly measured in miles per gallon (mpg). The fuel

lina2011 [118]

Answer:

0.7881 = 78.81% probability that a randomly chosen Ford truck outperforms a randomly chosen GM truck in terms of fuel efficiency

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

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

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

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.

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, and the standard deviation is the square root of the sum of the variances.

The fuel efficiency of Ford trucks is found to follow a normal distribution with mean 20 mpg and a standard deviation of 3 mpg.

This means that $\mu_{F} = 20, \sigma_{F} = 3$