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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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New York City is located about 40˚ north of the equator. If Earth's radius is about 4000 miles, approximately how many miles sou
qwelly [4]

Answer:

The answer is "2793 miles"

Step-by-step explanation:

In this firstly we convert degrees to radians, which can be defined as follows:

\to \theta =\frac{40^{\circ} \times \pi }{180^{\circ}}

       =\frac{ 2\pi  }{9}

Now calculating the distance:

=\frac{2\pi }{9} \times  4000\\\\= \frac{8000 \pi }{9}

=\frac{8000\times 3.14 }{9}\\\\ = \frac{25120}{9}\\\\=2793 \ miles

4 0
3 years ago
You want to help build an awards podium for a track meet. If the podium has the dimensions shown, what is its volume?
Dennis_Churaev [7]

Answer:

18

Step-by-step explanation:

4 0
3 years ago
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I need help due in 10 minutes ah!
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Answer:

30

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If CUB is 78 and that’s the full angle just to 48 minus 78 and you get your answer.

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Explain how a bar model can be used to show a subtraction problem
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The amount of money you have each month will be subtracted by the amount that you spend then you would put amount you spent on a bar graph alond with the amount you had
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3 years ago
Q5 Q6.) Find the exact value of the six trigonometric functions of theta.
lilavasa [31]
5y - 2x + 1 = 0.
5y = 2x-1.

y = 2/5 x - 2/5

this tells us that tan(theta) = 2/5
sin(theta)/sqrt(1-sin^2(theta)) = 2/5
x/sqrt(1-x^2)=2/5
x^2/(1-x^2)=4/25
25x^2=4-4x^2
29x^2=4
x^2=4/29
x = -2/sqrt(29) because quadrant III
cos(x) = sqrt(1-4/29) = -5/sqrt(29)


tan(theta)=2/5
cos(theta)=-5/sqrt(29)
sin(theta)=-2/sqrt(29)
cot(theta)=5/2
sec(theta)=-sqrt(29)/5
csc(theta)=-sqrt(29)/2



5 0
3 years ago
Read 2 more answers
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