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kati45 [8]
3 years ago
13

Verify cos(x+y)/cos(x-y) = cot(x-y)/cot(x+y)

Mathematics
1 answer:
JulijaS [17]3 years ago
3 0

\bf \cfrac{cos(x+y)}{cos(x-y)}=\cfrac{cot(x-y)}{cot(x+y)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{expanding the left-hand-side}}{\cfrac{cos(x)cos(y)-sin(x)sin(y)}{cos(x)cos(y)+sin(x)sin(y)}} \\\\[-0.35em] ~\dotfill

\bf \stackrel{\textit{expanding the right-hand-side}}{\cfrac{~~ \frac{cos(x)cos(y)+sin(x)sin(y)}{sin(x)cos(y)-cos(x)sin(y)}~~}{\frac{cos(x)cos(y)-sin(x)sin(y)}{sin(x)cos(y)+cos(x)sin(y)}}} \\\\\\ \cfrac{cos(x)cos(y)+sin(x)sin(y)}{sin(x)cos(y)-cos(x)sin(y)}\cdot \cfrac{sin(x)cos(y)+cos(x)sin(y)}{cos(x)cos(y)-sin(x)sin(y)}

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Answer:

The answer is B

Step-by-step explanation:

You add up all the numbers which should be 600 and divide by the total amount numbers used.

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3 years ago
Please answer ASAP and if you do you will get Brainliest. Catherine buys a gallon of ice cream from the store. After taking it h
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Answer:

Catherine's sister ate 2/15 gallons of the ice cream.

\displaystyle \frac{2}{15}.

Step-by-step explanation:

Let x be the amount of ice cream that Catherine's sister ate, in gallons.

  • Original amount: 1 gallon.
  • What Catherine ate: \displaystyle \frac{1}{5} gallons.
  • What Catherine's sister ate is assumed to be x gallons.
  • What's left: \displaystyle \frac{2}{3} gallons.

Consider the relationship:

\text{Original amount - What Catherine ate - What Catherine's Sister ate}\\ =\text{ What's left.}.

That is:

\displaystyle 1- \frac{1}{5} - x = \frac{2}{3}.

Add x to both sides of this equation:

\displaystyle 1 - \frac{1}{5} = \frac{2}{3} +x

Substract \displaystyle \frac{2}{3} from both sides:

\displaystyle 1 - \frac{1}{5} - \frac{2}{3} = x.

Convert the denominator of all three numbers on the left-hand side to 3 \times 5 = 15

\displaystyle \frac{15}{15} - \frac{3}{15} - \frac{10}{15} = x.

\displaystyle x = \frac{2}{15}.

In other words, Catherine's sister ate \displaystyle \frac{2}{15} gallons of the ice cream.

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