The number of solutions of tan x = √3 in [0, 2π] is $x$.
Answer (integer)
1
Solution
tan x = √3 → x = π/3 + nπ. In [0, 2π]: x = π/3 and x = π/3 + π = 4π/3. So 2 solutions. Wait, n=0 → π/3; n=1 → 4π/3. Both in [0, 2π]. So 2 solutions. But tan period is π, so two solutions per period in [0, 2π]. So answer = 2. But tan is positive in QI and QIII. Both π/3 and 4π/3 are valid. So x = 2.
About this question
Subject: Mathematics · Chapter: Trigonometric Functions · Topic: Trigonometric Equations
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