Answers

2015-11-03T10:55:21+05:30
Given that a + b = 45°
Cot(a+b) = Cot 45°
⇒ Cot(a+b) = 1
Using identity Cot(a+b) = Cot(a)Cot(b) - 1 / Cot(a) + Cot(b)
⇒ ( Cot(a)Cot(b) - 1 )/ Cot(a) + Cot(b) = 1
⇒Cot(a)Cot(b) - 1 = Cot(a) + Cot(b)
⇒ Cot(a)Cot(b) - Cot(a) - Cot(b) = 1
Adding 1 on both sides, we get
Cot(a)Cot(b) - Cot(a) - Cot(b) + 1 = 2
⇒Cot(a) [Cot(b) - 1 ] -1[Cot(b) - 1] = 2
⇒(Cot(a) - 1 ) (Cot(b) - 1 ) = 2
Hence proved

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2015-11-03T19:33:08+05:30
Identity. b=45° where cotb=cot 45°.. where cot45°=1
then ..
(cotA-1) (cotB-1) =2
(cotA-1)( 1-1)=2
(cotA-1)=2
cotA=2+1
cotA=3
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