Question

Cos2A + cos2A cot2A = cot2A​

Answer 1

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