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Question
Find the general solution of the following equation:
sin 2θ = `1/2`
Solution
The general solution of sin θ = sin α is
θ = nπ + (– 1)nα, n ∈ Z.
Now,
sin 2θ = `1/2`
∴ sin 2θ = `sin pi/(6) ...[ ∵ sin pi/(6) = (1)/(2)]`
∴ the required general solution is given by
2θ = nπ + (- 1)n `(pi/6)`, n ∈ Z.
i.e. θ = `(npi)/(2) + (- 1)^n (pi/12)`,n ∈ Z.
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