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If cosx . cosy + sinx . siny = –1 then cosx + cosy is
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- –2
- 1
- 0
- 2
Correct Option: C
cosx . cosy + sinx. siny = –1
⇒ cosx . cosy + 1 = – sinx . siny On squaring both sides, (cosx . cosy + 1)² = sin²x sin²y
⇒ cos²x . cos²y + 2cosx . cosy + 1 = (1 – cos²x) (1 – cos²y)
⇒ cos²x . cos2y + 2 cosx. cosy + 1 = 1 – cos²x – cos²y + cos²x . cos²y
⇒ cos²x + cos2y + 2cosx . cosy = 0
⇒ (cosx + cosy)² = 0
⇒ cosx + cosy = 0
