IPMAT Indore 2019 (SA) - The number of pairs (x, y) satisfying the equation x + y = (x + y) and |x| + |y| = 1 is | PYQs + Solutions

IPMAT Indore 2019

Geometry

Trigonometry

Hard

The number of pairs $(x, y)$ satisfying the equation $\sin x + \sin y = \sin(x + y)$ and $|x| + |y| = 1$ is

Entered answer:

✅ Correct Answer: 6

Key Insight: The reason we select only one of

x

y

as negative (not both) is because we want to find all distinct pairs that satisfy

|x| + |y| = 1

, and having both negative would create redundant counting.

When both

x

and

y

are negative, we get the same equation as when both are positive (since we're dealing with absolute values), so we only need to consider cases where at most one variable is negative to avoid double-counting the same geometric points.

IPMAT Indore 2019 (SA) PYQs

The number of pairs (x,y)(x, y)(x,y) satisfying the equation sin⁡x+sin⁡y=sin⁡(x+y)\sin x + \sin y = \sin(x + y)sinx+siny=sin(x+y) and ∣x∣+∣y∣=1|x| + |y| = 1∣x∣+∣y∣=1 is

Keyboard Shortcuts

The number of pairs $(x, y)$ satisfying the equation $\sin x + \sin y = \sin(x + y)$ and $|x| + |y| = 1$ is