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3 years ago

Cos2A + cos2A cot2A = cot2A

Mathematics

1 answer:

Vlad [161]3 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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Answer:

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Step-by-step explanation:

Step 1:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

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step 2:-

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on simplification, we will use formula

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Cos2A + cos2A cot2A = cot2A​

Cos2A + cos2A cot2A = cot2A