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sashaice [31]
3 years ago
12

Prove that :( 1 + 1/

smiddle" class="latex-formula">)(1 + 1/cot^{2}A) = 1/sin^{2}A - sin^{4}A
Mathematics
1 answer:
Aliun [14]3 years ago
3 0

Answer:

See explanation

Step-by-step explanation:

Simplify left and right parts separately.

<u>Left part:</u>

\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

<u>Right part:</u>

\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

Since simplified left and right parts are the same, then the equality is true.

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Bad White [126]
4n = 3m - 1

4n = 3m - 1
Subtract 3m from both sides.
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Subtract 4n from both sides.
-3m = -4n - 1
Divide both sides by -3.
m = 4/3n + 1/3

m = 4/3n + 1/3
4 0
3 years ago
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Answer:

C(2,5)

Step-by-step explanation:

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1. Match the polynomial identity to the correct answer.
Katen [24]

Answer:

a: (a-b)(a+b);b: (a-b)(a^{2}+ab+b^{2});  c: (a^{2} +2ab+b^{2}); d: (a+b)(a^{2}- ab+b^{2})

Step-by-step explanation:

Given the expressions all that is required is to expand them (using the distributive property) to see which answers they match up to:

For a: (a-b)(a+b)=a^{2} +ab-ab-b^{2} =a^{2}-b^2

For b: (a-b)(a^2+ab+b^2)=a^3+a^2b+ab^2-a^2b-ab^2-b^3=a^3-b^3

For c calculate the square of a sum: (a+b)^2=a^2+ab+ab+b^2

(add like terms) c: a^2+2ab+b^2

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5 0
3 years ago
when all the kids who tried out for soccer were divided into teams of 15 players, there were exactly eight teams. how many kids
seropon [69]
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5 0
4 years ago
3. The cost of the city permits needed to build this building is 150,000 no matter how many floors with
natima [27]

Answer:

P(x) = 150000

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Step-by-step explanation:

Given

Cost = 150000

Solving (a): The cost function:

From the given parameter, it shows that the number of floor has no effect on the floors.

So, represent the floors with x.

The cost function is:

P(x) = 150000

Solving (b): The slope and its interpretation

A function is represented as:

f(x) = b + mx

Where:

m=slope

By comparing: f(x) = b + mx to P(x) = 150000

m = 0

So:

Slope = 0

<em>What it means is that, no matter the number of floors, the cost remains unchanged.</em>

4 0
3 years ago
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