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IPMAT Indore 2023 - QA (MCQ) Q38 Explanation
December 31, 2024
Explanation
(c)
cos α+cos β=1⋯(i)
Let sin α−sin β=x…... (ii)
Squaring & adding - (i) & (ii) we get,
cos^2α + cos^2β + 2cosαcosβ = 1
sin^2α + sin^2β − 2sinαsinβ = x^2
(cos^2α + sin^2α) + (cos^2β + sin^2β) + 2(cosα ⋅ cosβ − sinα ⋅ sinβ)
=1 + x^2
1 + 1 + 2cos(α+β) = 1+x^2
x^2 = 1+2cos(α+β)
x = √1+2cos(α+β)
xmax = √1 + 2[cos (α+β)]max
xmax =√1 + 2 × 1 = √3 Ans.
Note: cosAcosB − sinA sinB = cos(A+B)
& −1 ≤ cos θ ≤1