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Question

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

A
αβ=π
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B
α+γ=3π
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C
β+γ=2π
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D
αγ=π
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Solution

The correct option is C β+γ=2π
Solutions of cotx=3 in [0,2π] are
x=ππ6 and 2ππ6
x=5π6,11π6 ...(1)

Solutions of cosec x=2 in [0,2π] are
sinx=12x=π+π6,2ππ6x=7π6,11π6 ...(2)

From (1) and (2), we get
α=11π6, β=5π6, γ=7π6αβ=π α+γ=3π β+γ=2π αγ=2π3

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