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Question

# Match the equations with their general solutions. (n∈I)

A
nπ+tan12
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B
nπ+(-1)nπ3
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C
2nπ±2π3
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D
nππ4
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Solution

## The expression involving an integer 'n' which gives all solutions of a trigonometric equation is called general solution. 1. tan x = 2 tan x = tan {tan−1 (2) } General solution when tan x = tan α x = nπ + α So general solution is x = nπ + tan−1 (2) n ∈ I 2. sin x = √32 sin x = sin π3 x = nπ + (−1)n π3 n ∈ I 3. cos x = - 12 cos x = cos 2π3 x = 2nπ ± 2π3 n ∈ I 4. cot x = -1 cot x = cot(- π4) x = nπ - π4 n ∈ I

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