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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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cupoosta [38]

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We know that the total cost can not be $2 more or less than $36

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Let's look at all the options and see which equation matches the above inequality.

A) |36+6x| ≤ 2

Since the above is a mod function, it can be written as:

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This also doesn't match with the required inequality. Hence, this option is not correct

C) |6x-2|<36

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This also doesn't match with the required inequality. Hence, this option is not correct

D) |36-6x| ≤ 2

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Multiplying the above by -1

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5 is 4% of 125.
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