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Question
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
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Solution
The general solution of cos θ = cos α is
θ = 2nπ ± α, n ∈ Z.
Now,
sec θ = √2
∴ cos θ = `(1)/sqrt(2)`
∴ cos θ = cos `pi/(4) ...[∵ cos pi/(4) = (1)/sqrt(2)]`
∴ the required general solution is
θ = 2nπ ± `pi/(4)`, n ∈ Z.
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