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Maths Straight Line Mix Single Correct MCQ

Published on: August 14, 2026

If sin ( α + β ) sin ( α – β ) = sin γ (2 sin β + sin γ ), 0 < α , β , γ < π, then the family of lines sin α x + sin β y + sin γ = 0 passes through

(–1, 1)

(1 , 1)

(1, –1)

(–1, –1)

Text Solution

Verified by Experts

The correct answer is:

sin ( α + β ) sin ( α – β ) = sin γ (2 sin β + sin γ )

(2 sin β + sin γ )

⇒ sin 2 α – sin 2 β = 2 sin β sin γ + sin 2 γ

⇒ sin 2 α – (sin β + sin γ ) 2 = 0

⇒ (sin α – sin β – sin γ ) (sin α + sin β + sin γ ) = 0

Since, 0 < α, β, γ < π

So, sin α + sin β , sin γ > 0

sin α + sin β + sin γ ≠ 0

So, sin α – sin β – sin γ = 0

or, (–1) sin α + 1 . sin β + sin γ = 0

Hence x sin α + y sin β + sin γ = 0

passes through (–1, 1).

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