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Elan Coil [88]
3 years ago
7

(sin teta + sec teta)^ + (cos teta+ cosec teta )^ = (1 + sec x cosec)^

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
4 0
(sin\theta+sec\theta)^2+(cos\theta+cosec\theta)^2=(1+sec\theta\ cosec\theta)^2\\\\L=sin^2\theta+2sin\theta\cdot\frac{1}{cos\thewta}+\frac{1}{cos^2\theta}+cos^2\theta+2cos\theta\cdot\frac{1}{sin\theta}+\frac{1}{sin^2\theta}\\\\=(sin^2\theta+cos^2\theta)+\frac{2sin\theta}{cos\theta}+\frac{2cos\theta}{sin\theta}+\frac{1}{cos^2\theta}+\frac{1}{sin^2\theta}

=1+\frac{2sin^2\theta+2cos^2\theta}{sin\theta\ cos\theta}+\frac{sin^2\theta+cos^2\theta}{sin^2\theta\ cos^2\theta}\\\\=1+\frac{2(sin^2\theta+cos^2\theta)}{sin\theta\ cos\theta}+\frac{1}{sin^2\theta\ cos^2\theta}\\\\=1+\frac{2}{sin\theta\ cos\theta}+\frac{1}{sin^2\theta\ cos^2\theta}\\\\=1^2+2sec\theta\ cosec\theta+sec^2\theta\ cosec^2\theta\\\\=(1+sec\theta\ cosec\theta)^2=R
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The events committee buys 80 flowers for a school dance. The flowers are a combination of carnations and roses. Each carnation c
Slav-nsk [51]

Answer:

64 carnations and 16 roses.

Step-by-step explanation:

The events committee buys 80 flowers

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Each carnation costs $0.50 and each rose costs $2.50

The committee spends a total of $72

<u>Solution:</u>

<u />

Let there be  (c) carnations and (r) roses.

So,

c + r = 80 flowers

and $0.50c + $2.50 = $72

This forms a simultaneous equation:

c + r = 80 ... (i)

0.5c + 2.5r = 72 ... (ii)

Multiplying equation (i) by 0.5 and equation (ii) by 1 gives;

0.5c + 0.5r = 40 ... (i)

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Subtracting (i)  from (ii) gives;

0c + 2r = 32

2r = 32

r = 32 ÷ 2 = 16

Therefore, there are 16 roses

and 80 - 16 = 64 carnations

7 0
3 years ago
Round 13 to the nearest 10.
mr Goodwill [35]

Round down to 10. 13 goes to 10.

3 0
3 years ago
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A notary receives $ 3500 for elaborating a title property and $2000 for the constitutive act of an enterprise. In a month did a
Andrew [12]

Answer:

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Step-by-step explanation:

Let the number of titles be t and the number of acts be a

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2000(22-t) + 3500t = 53,000

44,000 - 2000t + 3500t = 53,000

1,500t = 53000-44000

1500t = 9000

t = 9000/1500

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= 22-6 = 16

5 0
3 years ago
Which image shows a plane slicing a double-napped cone to produce a hyperbola?<br><br> Answer is D
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The <u>second image</u> in the diagram is a hyperbola. As can be seen, the plane cutting the cone can be at any angle but never equal to the slant angle of the cone. This has a very important implication. The plane cuts both cones of the double-napped cone. The third double-napped cone of Figure 3 shows two hyperbolas.

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