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in Mathematics by (75.1k points)

If cosx + cosy = 0 and sinx + siny = 0 then  cos(x – y) = ________ 

(a) 1

(b) (1/2)

(c) – 1

(d) – (1/2)

1 Answer

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Best answer

The correct option (c) – 1

Explanation:

cos(x – y) = cosx ∙ cosy + sinx ∙ siny

also (cosx + cosy)2 + (sinx + siny)2 = 0

∴ cos2x + cos2y +sin2x + sin2y + 2(cosx cosy) + 2(sinx siny) = 0

∴ 2 + 2(cosx ∙ cosy + sinx ∙ siny) = 0

∴ cos(x – y) = – 1.

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