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jasenka [17]
3 years ago
10

Tan^2x+sec^2x=1 for all values of x. true or false?

Mathematics
2 answers:
amid [387]3 years ago
5 0

This is not true.

\tan^2x+\sec^2x=\dfrac{\sin^2x}{\cos^2x}+\dfrac1{\cos^2x}=\dfrac{1-\cos^2x+1}{\cos^2x}=2\sec^2x-1

2\sec^2x-1=1\implies\sec^2x=1\implies\sec x=\pm1\implies x=n\pi

where is n is any integer. So suppose we pick some value of x other than these, say x=\dfrac\pi4. Then

\tan^2\dfrac\pi4+\sec^2\dfrac\pi4=1+2=3\neq1

padilas [110]3 years ago
3 0

The trigonometrical identity says : 1+tan^2x = sec^2 x that means

sec^2 x - tan^2 x = 1

However in our question, its tan^2 x + sec^2 x or say sec^2 x + tan^2 x = 1 which is completely against the identity.

Hense answer is False.

Additional information: There is, with a little difference, as equation which is true ie tan^2 x + sec x = 1 for some values of x.

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The <em><u>correct answer</u></em> is:

Corresponding (for both blanks)

Explanation:

Corresponding angles are angles that are in the same relative position to both the parallel line they are on and the transversal.  In this case, SQU and WRS are both above the parallel line they are on and on the same side of the transversal; this makes them corresponding angles.  This also means it is the corresponding angles postulate.

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3 years ago
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LenaWriter [7]

Answer:

0.73 N to 2 dp.

Step-by-step explanation:

F = k/d^2   where k is a constant , F = force and d = distance.

Substituting:

0.36 = k / (6)^2

k = 36*0.36 = 12.96 s the equation is F = 12.96 / d^2.

When d = 4.2 :

F = 12.96 / 4.2^2

F = 0.73 Newtons to 2 dp.

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3 years ago
It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken to estimate
Hitman42 [59]

Answer:

The minimum sample size is n = 75 so that the desired margin of error is 5 or less.                          

Step-by-step explanation:

We are given the following in the question:

Population variance = 484

Standard deviation =

\sigma^2 = 484\\\sigma =\sqrt{484} = 22

Confidence level = 0.95

Significance level = 0.05

Margin of error = 5

Formula:

Margin of error =

E = z\times \dfrac{\sigma}{\sqrt{n}}\\\\n = (\dfrac{z\times \sigma}{E})^2

z_{critical}\text{ at}~\alpha_{0.05} = 1.96

Putting values, we get

E\leq 5\\\\1.96\times \dfrac{22}{\sqrt{n}} \leq 5\\\\\sqrt{n} \geq 1.96\times \dfrac{22}{5}\\\\n \geq (1.96\times \dfrac{22}{5})^2\\\\n \geq 74.373

Thus, the minimum sample size is n = 75 so that the desired margin of error is 5 or less.

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2 years ago
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riadik2000 [5.3K]

Answer:

170°

Step-by-step explanation:

We can already see that measure ∠AD is equal to 85

A square has two halves, so this square will be added.

We will have to add 85 + 85 which equals 170°

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Answer:

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