Q.

Let α, β, γ be distinct real numbers lying in (0, π/2), then the equation 1x−sin⁡α+1x−sin⁡β+1x−sin⁡γ=0, has

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a

two distinct real roots

b

two equal roots

c

two imaginary roots

d

one real and one imaginary root.

answer is A.

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Detailed Solution

Let a=sin⁡α, b=sin⁡β, c=sin⁡γNote that a,b,c are distinct and 00                f(b)=(b-c)(b-a)<0and        f(c)=(c-a)(c-b)>0.Thus, f(x)=0 has a root in (a,b) and a root in (b,c).
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