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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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Find the point slope equation of the line using the point (6,9) and slope of 3/2
Natali [406]

Answer:

y=1.5x

Step-by-step explanation:

Use the equation y-y1=m(x-x1)

y-9=1.5(x-6)

y-9=1.5x-9

y=1.5x

8 0
3 years ago
Find the product of (x – a) and (x - b).
yawa3891 [41]

(x−a)(x−b)

=(x+−a)(x+−b)

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6 0
3 years ago
Five pounds is equal to 2.268 kilograms. How many kilograms is 2 pounds?
Tema [17]

Given:

5 pounds = 2.268 kilograms

To find:

The number of kilograms in 2 pounds.

Solution:

We have,

5 pounds = 2.268 kilograms

Divide both sides by 5.

1 pounds = \dfrac{2.268}{5} kilograms

1 pounds = 0.4536 kilograms

Multiply both sides by 2.

2 pounds = 2×0.4536 kilograms

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4 0
3 years ago
What is the domain and range of these two graphs .?
Vera_Pavlovna [14]

Answer:

5. D: (-4,3]  R: (5,-4] 7. D: (-1, 4] R: ( 5, -5]

Step-by-step explanation:

The domain is the point most to the left, and the point most to the right on the graph. The range is the point highest up and the point lowest down on the graph. You make a parentheses when the circle is hollow, but use a bracket when the circle is filled.

5 0
3 years ago
Find the perimeter of a rectangle if one of its sides is 14 and the area is 98
Ratling [72]

Answer:

42

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7 0
3 years ago
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