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Question:

Find the general solution: sec²2x = 1 - tan2x

Solution:

sec²2x = 1 - tan2x ⇒ 1 + tan²2x = 1 - tan2x ⇒ tan2x(tan2x + 1) = 0 ⇒ tan2x = 0, tan2x = -1 ⇒ 2x = nπ, 2x = nπ - π/4 ⇒ x = nπ/2, x = nπ/2 - π/8