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Find the general solution of the equation sin x = tan x. |
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Answer» sin x = tan x ∴ sin x = \(\frac{sin\,x}{cos\,x}\) ∴sin x cos x - sin x = 0 ∴ sin x (cos x - 1) = 0 ∴ sin x = 0 or cos x = 1 ∴ sin x = sin 0 or cos x = cos 0 Since, sin θ = 0 implies θ = nπ and cos θ = cos α implies θ = 2nπ ± α , n ∈ Z. ∴ x = nπ or x = 2mπ ± 0 ∴ The required general solution is x = nπ or x = 2mπ, where n, m ∈ Z. |
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