Given that \(\cos x + \cos y = 1\), the range of \(\sin x - \sin y\) is
Question and options
Given that , the range of is
Answer and explanation
Correct answer: D - \([-\sqrt{3}, \sqrt{3}]\)
(cos x + cos y)^2 + (sin x - sin y)^2 = 2 + 2cos(x+y), so (sin x - sin y)^2 = 1 + 2cos(x+y) <= 3. Attained at x = 60, y = -60 degrees (gives sqrt3) and symmetrically; range [-sqrt3, sqrt3].
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IPMAT Indore
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