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प्रश्न
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
उत्तर
`sqrt(3)` cosec θ + 2 = 0
`sqrt(3)` cosec θ = - 2
cosec θ = `(-2)/sqrt(3)`
sin θ = `-sqrt(3)/(2)`
sin θ = `-sin(pi/3)`
sin θ = `sin(pi + pi/3)` and sin θ = `sin (2pi - pi/3)`
sin θ = `sin ((4pi)/3)` and sin θ = `sin ((5pi)/3)`
= `[therefore 0≤ (4pi)/3 < 2pi and 0≤ (5pi)/3< 2pi]`
θ = `(4pi)/(3)` and θ = `(5pi)/(3)`
Principal solutions one `(4pi)/(3)` and `(5pi)/(3)`.
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