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Alborosie
3 years ago
12

Prove tan(x - (π / 4)) = (sin x – cos x) / (cos x + sin x) by filling in the reasons in the table below.

Mathematics
1 answer:
Mrac [35]3 years ago
8 0

No way to know what reasons you're supposed to choose from...

By definition of tangent,

\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin\left(x-\frac\pi4\right)}{\cos\left(x-\frac\pi4\right)}

The angle sum identities give

\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x\cos\frac\pi4-\cos x\sin\frac\pi4}{\cos x\cos\frac\pi4+\sin x\sin\frac\pi4}

cos\dfrac\pi4=\sin\dfrac\pi4=\dfrac1{\sqrt2}, so we can cancel those terms to get

\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x-\cos x}{\sin x+\cos x}

as required.

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(8y²)(-3x²y²)(2/3xy⁴)<br><br> HELP PLEASEEEEEEEE
IRINA_888 [86]

Step-by-step explanation:

1 Remove parentheses.

8{y}^{2}\times -3{x}^{2}{y}^{2}\times \frac{2}{3}x{y}^{4}

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2 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}

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\frac{8{y}^{2}\times -3{x}^{2}{y}^{2}\times 2x{y}^{4}}{3}

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3 Take out the constants.

\frac{(8\times -3\times 2){y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}

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\frac{(-24\times 2){y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}

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(−24×2)y

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y

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5 Simplify -24\times 2−24×2 to -48−48.

\frac{-48{y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}

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x

6 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

a

x

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a+b

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\frac{-48{y}^{2+2+4}{x}^{2+1}}{3}

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7 Simplify 2+22+2 to 44.

\frac{-48{y}^{4+4}{x}^{2+1}}{3}

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\frac{-48{y}^{8}{x}^{3}}{3}

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2 years ago
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Then (y-7)y=60, or y^2 - 7y - 60 = 0.  Use the quadratic formula to (1) determine whether y has real values and (2) to determine those values if they are real:

discriminant = b^2 - 4ac; here the discriminant is (-7)^2 - 4(1)(-60) = 191.  Because the discriminant is positive, this equation has two real, unequal roots, which are
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y = -------------------------
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and 

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y = ------------------------- = 3.41 (approximately)
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Unfortunately, this doesn't make sense, since the LCM of two numbers is generally an integer.


Try thinking this way:  If the LCM is 60, then xy = 60.  What would happen if x=5 and y=12?  Is xy = 60?  Yes.  Is 5 seven less than 12?  Yes.






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