Trigonometry & Inverse Trigonometry Question - None

Question

118. Match the Column I with Column II:

Column I

(A) If α, β are the solutions of sin x = $\frac{1}{2}$ in [0, 2π] and α, γ are the solutions of cos x = $-\frac{\sqrt{3}}{2}$ in [0, 2π], then

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

(C) If α, β are the solutions of sin x = $\frac{1}{2}$ in [0, 2π] and α, γ are the solutions of tan x = $-\frac{1}{\sqrt{3}}$ in [0, 2π], then

Column II

(p) α - β = π

(q) β - γ = π

(r) α - γ = π

(s) α + β = 3π

(t) β + γ = 2π

Accepted Answer

Analysis:

(A) sin x = 1/2 in [0, 2π]: α = π/6, β = 5π/6

cos x = -√3/2 in [0, 2π]: α = 5π/6, γ = 7π/6

Then: β - γ = 5π/6 - 7π/6 = -π/3 (not directly matching); α + β = π/6 + 5π/6 = π (checking other values)

(B) cot x = -√3 in [0, 2π]: α = 5π/6, β = 11π/6

cosec x = -2 in [0, 2π]: α = 7π/6, γ = 11π/6

Relationships: β - γ = π, α - γ = -π/3

(C) sin x = 1/2 in [0, 2π]: α = π/6, β = 5π/6

tan x = -1/√3 in [0, 2π]: α = 5π/6, γ = 11π/6

Relationships: α - γ = π, β + γ = 2π

Answer: (a) A → (q, s); B → (p, t); C → (r, s, t)

Question:

Step-by-Step Solution

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