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3 years ago

Helpp!!!(1-sin2A)(1+cot2A)=cot2A

Mathematics

1 answer:

lord [1]3 years ago

4 0

This isn't an identity, so I assume you have to solve the equation.

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

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

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

sin(2A) + cos(2A) = 1

Multiply both sides by 1/√2, which we want to do because cos(π/4) = sin(π/4) = 1/√2. This gives

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

Then condense the left side as

sin(2A + π/4) = 1/√2

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

2A = 2nπ or 2A = π/2 + 2nπ

A = nπ or A = π/4 + nπ

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