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If cotA+cotB=a, tanA+ tanB=b a+b=c then show (a-b) tan c= ab

If
cotA+cotB=a, tanA+ tanB=b
a+b=c
then show  (a-b) tan c= ab

Grade:11

2 Answers

Lab Bhattacharjee
121 Points
7 years ago
a=\cot A+\cot B=\dfrac{\tan B+\tan A}{\tan B\tan A}=\dfrac b{\tan B\tan A} \\ \implies\tan A\tan B=\dfrac ba \\ \tan C=\tan(A+B)=\dfrac{\tan A+\tan B}{1-\tan A\tan B}=\dfrac b{1-\dfrac ba}=?
Raghu Vamshi Hemadri
72 Points
7 years ago
a=\cot A+\cot B=\dfrac{\tan B+\tan A}{\tan B\tan A}=\dfrac b{\tan B\tan A} \\ \implies\tan A\tan B=\dfrac ba \\ \tan C=\tan(A+B)=\dfrac{\tan A+\tan B}{1-\tan A\tan B}=\dfrac b{1-\dfrac ba}=?

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