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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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Helen [10]
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4 0
3 years ago
Expand 3(5y-3) can someone answer this please
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Answer:

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Step-by-step explanation:

3(5y-3)

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7 0
3 years ago
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Please Help!
Nezavi [6.7K]

Let the first number = x

The second number would be 5x

The third number would be 100x

Add:

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Simplify:

7x + 100 = 296

subtract 100 from both sides:

7x = 196

Divide both sides by 7

X = 196 / 7

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3 0
3 years ago
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7а — За +2а — а = 16
dezoksy [38]

Answer:

(7a-3a)+(2a-a)=16

4a+a or 1a =16

5a=16

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Step-by-step explanation:

solving like terms or substract are same

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8 0
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