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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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Determine whether the geometric series is convergent or divergent. 9 + 8 + 64/9 + 512/81 + ..... If it is convergent, find its s
Westkost [7]

Answer:

Convergent; 81

Step-by-step explanation:

r = term2/term1 = 8/9

8/9 < 1 so convergent

Sum = 9/(1 - 8/9)

= 9/(1/9) = 81

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3 years ago
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2 years ago
A dealer buys oranges for 100000, he sold 60% of them for buying price, he sold 50% of the remaining for profit of 60% then he s
suter [353]

Based on the amount of oranges bought, those sold at a profit and those sold at a loss, the overall profit is 14.2%

<h3>What is the overall profit?</h3>

Assume that the buying price was $1 each.

The amount earned from 60% of them is:

= 60% x 100,000 x 1

= $60,000

The profit from selling 50% of the remaining is:

= (50% x 40,000) x 1.60

= $32,000

The loss from selling the other 50%:

= (50% x 40,000) x 0.90

= $22,222.22

Total selling price:

= 60,000 + 32,000 + 22,222.22

= $114,222.22

Total profit:

= (114,222.22 - 100,000) / 100,000

= 14.2%

Find out more on sales profit at brainly.com/question/19104371

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7 0
1 year ago
What is the solution of (3x + 8)/(x - 4) &gt;= 02
ipn [44]

Answer:

3x+8=0

x=-8/3The face of the denominator must be 0

And the face and denominator of the fraction must be positive

Step-by-step explanation:

4 0
3 years ago
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masha68 [24]
Y=7, i hope this helps:)
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