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JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1
If −π≤x≤π,−π≤y≤π-\pi \leq x \leq \pi,-\pi \leq y \leq \pi and cos⁡x+cos⁡y=2\cos x+\cos y=2, then the value cos⁡(x−y)\cos (x-y) is
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Correct option: C
1
Option C (1) is correct because the maximum value of cos⁡x\cos x and cos⁡y\cos y is 1, and their sum being 2 implies both must be 1, leading to x=y=0x=y=0 and cos⁡(x−y)=1\cos(x-y) = 1.

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