If cot2⁡Acot2⁡B=3, then the value of (2 - cos 2A) (2 - cos 2B) is ___________.

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answer is 3.

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Detailed Solution

(2−cos⁡2A)(2−cos⁡2B) =1+2sin2⁡A1+2sin2⁡B =1+2sin2⁡A+sin2⁡B+4sin2⁡Asin2⁡B …….. (1)Now, cot2⁡A cot2⁡B=3⇒ cos2⁡Acos2⁡B=3sin2⁡Asin2⁡B⇒ 1−sin2⁡A1−sin2⁡B=3sin2⁡Asin2⁡B⇒ sin2⁡A+sin2⁡B+2sin2⁡Asin2⁡B=1From (1), we get(2−cos⁡2A)(2−cos⁡2B)=1+2=3

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