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3 years ago

9

Which equation represents this statement?

2 answers:

MAXImum [283]3 years ago

4 0

2 n - 5 = 3

So A is the answer

Zolol [24]3 years ago

4 0

Answer:

5<3x2 $i think$

Step-by-step explanation:

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Hello! Verify the identity. Please show your work! Use trigonometric identities to verify each expression is equal.

RSB [31]

Answer:

See Below.

Step-by-step explanation:

We want to verify the identity:

$\displaystyle \csc^2 x -2\csc x \cot x +\cot ^2 x = \tan^2\left(\frac{x}{2}\right)$

Note that the left-hand side is a perfect square trinomial pattern. Namely:

$a^2-2ab+b^2=(a-b)^2$

If we let <em>a</em> = csc(x) and <em>b</em> = cot(x), we can factor it as such:

$\displaystyle (\csc x - \cot x)^2 = \tan^2\left(\frac{x}{2}\right)$

Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):

$\displaystyle \left(\frac{1}{\sin x}-\frac{\cos x }{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)$

Combine fractions:

$\displaystyle \left(\frac{1-\cos x}{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)$

Square (but do not simplify yet):

$\displaystyle \frac{(1-\cos x)^2}{\sin ^2x}=\tan^2\left(\frac{x}{2}\right)$

Now, we can make a substitution. Let <em>u</em> = <em>x</em> / 2. So, <em>x</em> = 2<em>u</em>. Substitute:

$\displaystyle \frac{(1-\cos 2u)^2}{\sin ^22u}=\tan^2u$

Recall that cos(2u) = 1 - sin²(u). Hence:

$\displaystyle \frac{(1-(1-2\sin^2u))^2}{\sin ^2 2u}=\tan^2u$

Simplify:

$\displaystyle \frac{4\sin^4 u}{\sin ^2 2u}=\tan^2 u$

Recall that sin(2u) = 2sin(u)cos(u). Hence:

$\displaystyle \frac{4\sin^4 u}{(2\sin u\cos u)^2}=\tan^2 u$

Square:

$\displaystyle \frac{4\sin^4 u}{4\sin^2 u\cos ^2u}=\tan^2 u$

Cancel:

$\displaystyle \frac{\sin ^2 u}{\cos ^2 u}=\tan ^2 u$

Since sin(u) / cos(u) = tan(u):

$\displaystyle \left(\frac{\sin u}{\cos u}\right)^2=\tan^2u=\tan^2u$

We can substitute <em>u</em> back for <em>x</em> / 2:

$\displaystyle \tan^2\left(\frac{x}{2}\right)= \tan^2\left(\frac{x}{2}\right)$

Hence proven.

3 0

3 years ago

What’s the square root of 3

belka [17]

According to my calculations. The answer to this question is 89

5 0

4 years ago

Read 2 more answers

1. The product of five and a number is 15

dedylja [7]

Answer:

Step-by-step explanation:

(1) $5x = 15$

Dividing both sides by $5$ will give us the answer:

$x = 3$

(2) $x + 6 = 16$

Subtracting both sides by $6$ will give us the answer:

$x = 10$

(3) $\frac{27}{x} = 9$

First let's multiply both sides by $x$

$27 = 9x$

Now, let's divide both sides by $9$ to get our answer:

$x = 3$

(4) $6x = 72$

Dividing both sides by $6$ will give us the answer:

$x = 12$

6 0

3 years ago

X+y=1<br> 2x-y=-2<br><br> Please help

Illusion [34]

Hi fren,

x=<span><span>−y</span>+<span>1
and for the second one...
</span></span>y=<span><span>2x</span>+<span>2

</span></span>x-intercept >> <span>(<span><span>−1</span>,0</span>)
</span>y-intercept >> <span>(<span>0,2)</span></span><span>

</span>

4 0

3 years ago

Read 2 more answers

20/4+8/3 answer? I don’t get the question

Bumek [7]

Answer:

Step-by-step explanation:

if you need to add 2 fractions

20/4+ 8/3

common denominator is 12

60/12+32/12=92/12= 7 8/12 =7 2/3

3 0

3 years ago

Read 2 more answers