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Question

If sin α, sin β, cos α are in GP, then roots of equation x2 sin β+2x cos β+sin β=0 are


A

Real

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B

imaginary

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C

depends on α, β, γ

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D

data insufficient

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Solution

The correct option is A

Real


sin α, sin β, cos α in GPsin2β=sin α cos α2 sin2β=2sin α cos α2 sin2β=sin 2αsin2β=12 sin 2x 0sin2β12 cosec2 β2
Given equation
x2 sin β+2x cos β+sin β=0x2+2x cot β+1=0 Δ=4 cot2β4=4(cot2 β1)=4(cosec2β2)=4(22)0
real roots


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