If A+B=225^(@), then find the value of (...

If `A+B=225^(@)`, then find the value of `(cotA)/(1+cotA)xx(cot B)/(1+cotB)`

Text Solution

Verified by Experts

The correct Answer is:

`1//2`

`(cotA)/(1+cotA)xx(cotB)/(1+cotB)`
`=(1)/((1+tanA)(1+tanB))`
`=(1)/(tan A+tan B+1+tan A tan B)`
Now, `tan(A+B)=tan225^(@)`
`rArr tanA+tanB=1-tan A tan B`
Hence, from Eq. i,
RHS`=(1)/(1-tan A tan B+1+tan A tan B)=(1)/(2)`

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