What is the circumference of a gummy

Prove that (Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A

iVinArrow [24]

Answer:

The answer is below

Step-by-step explanation:

We need to prove that:

(Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A.

Firstly, 1 / cos A = sec A, 1 / sin A = cosec A and tanA = sinA / cosA.

Also, 1 + tan²A = sec²A; sec²A - 1 = tan²A

$\frac{\sqrt{secA-1} }{\sqrt{secA+1} } +\frac{\sqrt{secA+1} }{\sqrt{secA-1} } =\frac{(\sqrt{secA-1)}(\sqrt{secA-1})+(\sqrt{secA+1)}(\sqrt{secA+1}) }{(\sqrt{secA+1})(\sqrt{secA-1}) } \\\\=\frac{secA-1+(secA+1)}{\sqrt{sec^2A-secA+secA-1} } \\\\=\frac{2secA}{\sqrt{sec^2A-1} } \\\\=\frac{2secA}{\sqrt{tan^2A} } \\\\=\frac{2secA}{tanA} \\\\=\frac{2*\frac{1}{cosA} }{\frac{sinA}{cosA} }\\\\= 2*\frac{1}{cosA}*\frac{cosA}{sinA}\\\\=2*\frac{1}{sinAA}\\\\=2cosecA$

7 0

3 years ago

Find the values of a and b such that

Varvara68 [4.7K]

Answer:

a = 1.5

b = 1.75

Step-by-step explanation:

First, we need to solve $(x+a)^2$ and replace the result in the initial equation as:

$x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b$

Then, this equality apply only if the coefficient of $x$ is equal in both sides and the constant is equal in both sides.

It means that we have two equations:

$3x=2ax\\4=a^2+b$

So, using the first equation and solving for a, we get:

$3x=2ax\\3=2a\\a=\frac{3}{2}=1.5$

Finally, replacing the value of a in the second equation and solving for b, we get:

$4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75$

3 0

3 years ago

1. Sally said that when you add or subtract positive or negative decimals, you can change the order of the decimals and still ge

Oduvanchick [21]

can you type the decimals in the comments

7 0

3 years ago

A card is picked up at random from a pack of 52 cards. Find the probability that it is a king or queen.

zalisa [80]

Total number of cards = 52
Total number of kings or queens = 8

P(King or Queen) = 8/52 = 2/13

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Answer: The probability is 2/13.
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3 0

3 years ago

The figure shown is a rectangle. The green shape in the figure is a square. The blue and white shapes are rectangles, and the ar

VikaD [51]

Answer:

A. (2 × 6) + (3 × 8) + 6²

72 sq. inches.

B. 9 in. by 8 in.

Step-by-step explanation:

The white shape has dimensions of 2 in. by 6 in. and the green shape is a square.

So, the dimension of the green shape is 6 in. by 6 in.

Therefore, the length of the blue shape is (6 + 2) = 8 in.

Now, given that the area of the blue shape is 24 sq. in.

So, the width of the blue shape is $\frac{24}{8} = 3$ in.

Now, if we consider the total figure, then area of the entire figure = area of the white shape + area of the green shape + area of the blue shape.

= (2 × 6) + (3 × 8) + 6² (Answer)

= 12 + 24 + 36

= 72 sq, inches. (Answer)

Now, the length of the entire figure is (6 + 3) = 9 in. and width of the entire figure is (2 + 6) = 8 in.

Therefore, the dimensions of the entire figure will be 9 in. by 8 in. (Answer)

5 0

3 years ago