If sin- sin- and cosin GP- then roots of the equation x2-2 x -1-0 are always

The correct option is D Real sin^2β = sinα cosα ⇒ cos2β = 1 sin2α≥ 0 Now, the discriminant of the given equation is 4cot^2β 4 ≥ 0 Roots are always real ...

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Standard XII

Mathematics

Expansions to Remove Indeterminate Form

If sinα, sinβ...

Question

If sin $α$ , sin $β$ and cosαare in GP, then roots of the equation $x^{2}$ + 2xcot $β$ +1 = 0 are always

equal

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Real

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Imaginary

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rational and unequal

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Solution

The correct option is B
Real

$s i n^{2} β = s i n α c o s α$

$\Rightarrow c o s 2 β = 1 - s i n 2 α \geq 0$

Now, the discriminant of the given equation is

$4 c o t^{2} β - 4 \geq 0$

Roots are always real

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If sin α, sin β and cosαare in GP, then roots of the equation x2 + 2xcotβ+1 = 0 are always

The correct option is B Real sin2β=sinαcosα ⇒cos2β=1−sin2α≥0 Now, the discriminant of the given equation is 4cot2β−4≥0 Roots are always real

If sin $α$ , sin $β$ and cosαare in GP, then roots of the equation $x^{2}$ + 2xcot $β$ +1 = 0 are always

The correct option is B
Real

$s i n^{2} β = s i n α c o s α$

$\Rightarrow c o s 2 β = 1 - s i n 2 α \geq 0$

Now, the discriminant of the given equation is

$4 c o t^{2} β - 4 \geq 0$

Roots are always real