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If A+B+C=pi/2, show that : cotA+cotB+cot...

If `A+B+C=pi/2`, show that : `cotA+cotB+cotC=cotA cotB cotC`

Text Solution

Verified by Experts

(a) `A+B+C=(pi//2)rArrA+B=(pi//2)-C`
`rArr tan(A+B)=tan(pi//2-C)`
`rArr (tan A+tanB)/(1-tanA tan B)=cotC`
Now convert all the terms cot and simplify.
(b) Replace `cot C` by `(1)/(tanC)` in Eq. i and simplify.
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