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2 years ago

Cos2A + cos2A cot2A = cot2A

Mathematics

1 answer:

Vlad [161]2 years ago

7 0

cos(2A) + cos(2A) cot(2A) = cot(2A)

cos(2A) + cos(2A) cot(2A) - cot(2A) = 0

cot(2A) sin(2A) + cos(2A) cot(2A) - cot(2A) = 0

cot(2A) (sin(2A) + cos(2A) - 1) = 0

cot(2A) = 0 or sin(2A) + cos(2A) - 1 = 0

cot(2A) = 0 or sin(2A) + cos(2A) = 1

cot(2A) = 0 or sin(2A) cos(π/4) + cos(2A) sin(π/4) = 1/√2

cot(2A) = 0 or sin(2A + π/4) = 1/√2

[2A = cot⁻¹(0) + nπ] or

[2A + π/4 = sin⁻¹(1/√2) + 2nπ or 2A + π/4 = π - sin⁻¹(1/√2) + 2nπ]

(where n is any integer)

[2A = π/2 + nπ] or

[2A + π/4 = π/4 + 2nπ or 2A + π/4 = 3π/4 + 2nπ]

[A = π/4 + nπ/2] or

[2A = 2nπ or 2A = π/2 + 2nπ]

[A = π/4 + nπ/2] or

[A = nπ or A = π/4 + nπ]

A = (1 + 2n) π/4 or A = nπ or A = π/4 + nπ

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2 years ago

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2 years ago

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Maurinko [17]

Using linear combination method, the solution to given system of equations are (-7, -15)

<h3>Solution:</h3>

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated

Addition is used when the two equations have terms that are exact opposites, and subtraction is used when the two equations have terms that are the same.

Given system of equations are:

2x - y = 1 ---- eqn 1

3x - y = -6 ------ eqn 2

Subtract eqn 2 from eqn 1

2x - y = 1

3x - y = -6

(-) -------------

-x = 7

Substitute x = -7 in eqn 1

2(-7) - y = 1

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y = -14 - 1 = -15

Thus the solution to given system of equations are (-7, -15)

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3 years ago

Cos2A + cos2A cot2A = cot2A​

Cos2A + cos2A cot2A = cot2A