If - are the solutions of x-3 in -0-2- and - are the solutions of cosec x-2 in -0-2- then

Solutions of x= √(3) in [0,2π] are x=π π6 and 2π π6 ⇒ x=5π6,11π6 ...(1) Solutions of cosec x= 2 in [0,2π] are ⇒sin x= 12 ⇒ x=π+π6,2π π6 ⇒ x=7π6,11π6 ...(2) ...

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Standard XII

Mathematics

Principal Solution of Trigonometric Equation

If α,β are th...

Question

If $α, β$ are the solutions of $cot x = - \sqrt{3}$ in $[0, 2 π]$ and $α, γ$ are the solutions of $cosec x = - 2$ in $[0, 2 π],$ then

α - β = π

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α + γ = 3 π

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β + γ = 2 π

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α - γ = π

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Solution

The correct option is C $β + γ = 2 π$
Solutions of $cot x = - \sqrt{3}$ in $[0, 2 π]$ are
$x = π - \frac{π}{6}$ and $2 π - \frac{π}{6}$
$\Rightarrow x = \frac{5 π}{6}, \frac{11 π}{6} . . . (1)$

Solutions of $cosec x = - 2$ in $[0, 2 π]$ are
$\Rightarrow sin x = - \frac{1}{2} \Rightarrow x = π + \frac{π}{6}, 2 π - \frac{π}{6} \Rightarrow x = \frac{7 π}{6}, \frac{11 π}{6} . . . (2)$

From $(1)$ and $(2)$ , we get
$α = \frac{11 π}{6}, β = \frac{5 π}{6}, γ = \frac{7 π}{6} ∴ α - β = π α + γ = 3 π β + γ = 2 π α - γ = \frac{2 π}{3}$

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If α,β are the solutions of cotx=−√3 in [0,2π] and α,γ are the solutions of cosec x=−2 in [0,2π], then

If $α, β$ are the solutions of $cot x = - \sqrt{3}$ in $[0, 2 π]$ and $α, γ$ are the solutions of $cosec x = - 2$ in $[0, 2 π],$ then