#### Question

Find the general solution of the equation sin x = tan x.

#### Solution

sin x = tan x

∴ sin x = sinx/cosx

∴ 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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#### APPEARS IN

Solution for question: Find the general solution of the equation sin x = tan x. concept: Trigonometric Functions - General Solution of Trigonometric Equation of the Type. For the courses HSC Arts, HSC Science (Electronics), HSC Science (General) , HSC Science (Computer Science)