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ZanzabumX [31]
3 years ago
14

Write the expression as either the sine, cosine, or tangent of a single angle. tan5x - tan2y / 1 + tan5x tan2y

Mathematics
1 answer:
Kryger [21]3 years ago
6 0
\bf \textit{Sum and Difference Identities}
\\\\
tan(\alpha + \beta) = \cfrac{tan(\alpha)+ tan(\beta)}{1- tan(\alpha)tan(\beta)}
\qquad
tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)}\\\\
-------------------------------\\\\
\cfrac{tan(5x)-tan(2y)}{1+tan(5x)tan(2y)}\implies tan(5x-2y)
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<u>George fell asleep when he had traveled 1/5 of the total distance, slept 3/5 of the distance and he awoke up when he's still 1/5 away from his grandma</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

George fell asleep a fifth of the way

He awoke up when he still had to travel a quarter of the distance that he had traveled while sleeping

2. For what part of the journey had he been asleep?

George fell asleep a fifth of the way: 1/5 of the total distance traveled and 4/5 of the distance away from his grandma

When he awoke up = 1/4 * 4/5 = 1/5

He had been asleep = 5/5 - 1/5 -1/5 = 3/5

<u>It means George fell asleep when he had traveled 1/5 of the total distance, slept 3/5 of the distance and he awoke up when he's still 1/5 away from his grandma</u>

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