In a triangle, the cosines of two angles are inversely proportional to the sides opposite the angles. the
triangle may be

isosceles

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equilateral

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right angled

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None of these

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Solution

The correct options are
A isosceles
B right angled
$a c o s A = b c o s B \Rightarrow 2 R s i n A c o s A = 2 R s i n B c o s B$
$\Rightarrow s i n 2 A = s i n 2 B$
$A = B$
or $2 A + 2 B = 180^{\circ} \Rightarrow A + B = 90^{\circ} \Rightarrow C = 90^{\circ}$
So the triangle is right angled triangle and it may be an isosceles triangle as well (90-45-45)

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In a triangle, the cosines of two angles are inversely proportional to the sides opposite the angles. thetriangle may be

The correct options are A isosceles B right angledacosA=bcosB⇒2RsinAcosA=2RsinBcosB⇒sin2A=sin2BA=Bor 2A+2B=180∘⇒A+B=90∘⇒C=90∘So the triangle is right angled triangle and it may be an isosceles triangle as well (90-45-45)

In a triangle, the cosines of two angles are inversely proportional to the sides opposite the angles. the
triangle may be