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Question
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
Solution
sin2 θ - cos2 θ = 1
∴ cos2 θ - sin2 θ = - 1
∴ cos2θ = cos π .....(1)
The general solution of cos θ = cos α is
θ = 2nπ ± α, n ∈ Z.
∴ the general solution of (1) is given by
2θ = 2nπ ± π, n ∈ Z.
∴ θ = nπ ± `pi/2`, n ∈ Z
Notes
The answer in the textbook is incorrect.
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