Question

cotA cotB=2 then proove
cos(a+b)/cos(a-b)=1/3

Answer 1

Hope it helps you...

Answer 2

$CotACotB = 2 \: (given )$

$\implies \frac{CosACosB}{SinA SinB } = 2$

$\implies CosACos B = 2SinA SinB \:---(1)$

$\red{ \frac{Cos(A+B)}{Cos(A-B)} }\\= \frac{CosA CosB - SinA Sin B }{ CosA CosB + Sin A Sin B } \\= \frac{ 2SinA SinB - SinASinB }{ 2SinASinB + SinA Sin B } \: [ From \: (1) ] \\= \frac{SinA SinB }{ 3 SinASinB } \\\green {= \frac{1}{3}} \\= RHS$

$Hence\: proved$

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