IPMAT 2019 - Quantitative Aptitude Question 36
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IPMAT 2019 - Quantitative Aptitude
cos x + cos y = 1
Squaring, we get cos2x+ cos2y + 2 cos x cos y = 1 ......(1)
Similarly, let sin x – sin y = p
Squaring, we get sin2 x + sin2 y – 2sin x sin y = p2 ......(2)
Adding (1) and (2)
cos2 x + sin2 x + cos2 y + sin2 y + 2(cos x cos y – sin x sin y) = 1 + p2
2 + 2 cos(x + y) = 1 + p2
p2 = 1 + 2 cos(x + y)
Since – 1 ≤ cos (x + y) ≤ 1
1 + 2x(– 1) ≤ p2 ≤ 1 + 2 × 1
– 1 ≤ p2 ≤ 3
A square can never be negative.
Hence O ≤ P2 ≤ 3
Since p2 ≤ 3
–√3 ≤ p ≤ √3