Best Online CAT Coaching

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