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Verify the identity

Thepotemich [5.8K]

<u>Given</u>:

Given that we need to prove the identity $\sin x+\sin x \tan ^{2} x=\tan x \sec x$

<u>Proof</u>:

Step 1: Factor out the common term sin x, we get;

$\sin x\left(1+\tan ^{2} x\right)=tan \ x \ sec \ x$

Step 2: Using the identity $1+tan^2 x=sec^2x$

$\sin x \sec ^{2} x=tan \ x \ sec \ x$

Step 3: Reciprocating sec x, we get;

$\sin x \cdot \frac{1}{\cos ^{2} x}=tan \ x \ sec \ x$

Step 4: Splitting the denominator, we have;

$\frac{\sin x}{\cos x} \cdot \frac{1}{\cos x}=tan \ x \ sec \ x$

Simplifying, we get;

$\tan x \sec x=\tan x \sec x$

Thus, the identity is proved.

5 0

3 years ago

In a study of 775 randomly selected medical malpracticelawsuits, it was found that 502 of them were dropped or dismissed. Use a

bulgar [2K]

By using a 0.05 significance level, we can conclude that there is sufficient evidence that most medical malpractice lawsuits are dropped or dismissed.

<h3>How to test the claim for the medical malpractice lawsuits?</h3>

Since we have to compare whether the sample proportion is greater than or lesser than the population proportion, a one-tailed test would be used. Also, we would calculate the sample proportion of medical malpractice lawsuits that are dropped or dismissed as follows:

Sample proportion, p = x/n

Sample proportion, p = 502/775

Sample proportion, p = 0.6477

Mathematically, the null and alternative hypothesis is given by:

H₀: p = 0.5

H₁: p > 0.5

For the test statistic can be calculated by using this mathematical expression:

$z=\frac{\hat{p}\;-\;p_o}{\sqrt{\frac{p_o(1-p_o)}{n }} }$

Where:

$\hat{p}$ represents the sample mean.
$p_o$ represents the mean.
n represents the number of subjects.

Substituting the given parameters into the formula, we have;

z = (0.6477 - 0.5)/√(0.5(1 - 0.5)/775)

z = 0.1477/√(0.25/775)

z = 0.1477/0.01796

z = 8.224.

For the p-value, we have:

p(z>8.224) = 0.0000

Therefore, the p-value (0.000) is less than the significance level α = 0.05. Based on this, we would reject the null hypothesis.

Read more on malpractice lawsuits here: brainly.com/question/13032617

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5 0

11 months ago

Find an equation of the line through (2,6) and parallel to y=2x+3

Setler [38]

Step-by-step explanation:

We first Find the Slope of the line y=2x+3

The Slope Intercept Form of the equation of a given line is:

y=mx+c

where m is the Slope of that line, and c is the Y intercept.

For this line, the Slope is 2

So the Slope of the line PARALLEL to y=2x+3 will also be 2. And we are given that it passes through the point (2,6)

The Point-Slope form of the Equation of a Straight Line is:

(y−k)=m⋅(x−h)

m is the Slope of the Line

(h,k) are the co-ordinates of any point on that Line.

Here, we have been given the coordinates (h,k) of 1 point on that line as (2,6)

And the Slope m is 2

Substituting the values of h,k and m in the Point-Slope form, we get

(y−2)=(2)⋅(x−6)

(y−2)=2⋅(x-6)

y−2=2x -12

y=2x -12 +2

y=2x-10

The graph will look like

graph{y=2x -10 10 [10, -10, 5, - 5]}

3 0

3 years ago

Simplify the expression <br><br> c+2+c+c+4

professor190 [17]

Answer:

2+4+ccc

Step-by-step explanation:

7 0

2 years ago

What is 175% of 14.2

LUCKY_DIMON [66]

175% of 14.2 is saying that

1.75(14.2)=24.9

Any questions please just ask. Thank you.

7 0

3 years ago

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