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ahrayia [7]
3 years ago
14

True or False? Tell whether the pair of ratios form a proportion. 8/12 and 14/21 Please explain why you chose what you chose​

Mathematics
1 answer:
erik [133]3 years ago
8 0

Answer:

True; The pair of ratios form a proportion.

Step-by-step explanation:

To tell whether these two ratios are proportional, we can simplify each of them

\frac{8}{12} =\frac{2}{3}

\frac{14}{21} =\frac{2}{3}

As both ratios simplify into the same ratio, they are proportional.

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. Evaluate tan(α + β) = sin(????+????) / cos(????+????) to show tan(???? + ????) = tan(????)+tan(????????) / 1−tan(????) tan(???
grandymaker [24]

Answer with Step-by-step explanation:

We are given that

tan(\alpha+\beta)

\frac{sin(\alpha+\beta}{cos(\alpha+\beta)}

By using formulatan x=\frac{sin x}{cos x}

\frac{sin\alpha cos\beta+sin\beta cos\alpha}{cos\alpha cos\beta-sin\alpha sin\beta}

By using property:sin(x+y)=sin x cosy+cos x sin y

cos(x+y)=cos x cosy-sin x siny

Divide numerator and denominator by cos\alpha cos\beta

Then, we get

\frac{\frac{sin\alpha}{cos\alpha}+\frac{sin\beta}{cos\beta}}{1-\frac{sin\alpha sin\beta}{cos\alpha cos\beta}}

tan(\alpha+\beta)=\frac{tan\alpha+tan\beta}{1-tan\alpha tan\beta}

Hence, proved

Substitute \alpha=\beta

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3 0
4 years ago
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