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प्रश्न
Find the general solution of the following equation:
sin θ = tan θ.
उत्तर
sin θ = tan θ
∴ sinθ = `"sinθ"/"cosθ"`
∴ sinθ cosθ = sinθ
∴ sinθ cosθ – sinθ = 0
∴ sinθ (cosθ – 1) = 0
∴ either sinθ = 0 or cosθ – 1 = 0
∴ either sinθ = 0 or cosθ = 1
∴ either sinθ = 0 or cosθ = cos0 ...[∵ cos 0 = 1]
The general solution of sin θ = 0 is θ = nπ, n ∈ Z and cosθ = cos α is θ = 2nπ ± α, where n ∈ Z.
∴ the required general solution is given by
θ = nπ, n ∈ Z or θ = 2nπ ± 0, n ∈ Z
∴ θ = nπ, n ∈ Z or θ = 2nπ, n ∈ Z.
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