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In A B C , if b^2+c^2=2a^2, then value ...

In ` A B C ,` if `b^2+c^2=2a^2,` then value of `(cotA)/(cotB+cotC)` is `1/2` (b) `3/2` (c) `5/2` (d) `5/2`

A

`(1)/(2)`

B

`(3)/(2)`

C

`(5)/(2)`

D

`(5)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(cotA)/(cotB cotC) = ((R(b^(2) + c^(2) -a^(2)))/(abc))/((R(a^(2) + c^(2) -b^(2)))/(abc) + (R(a^(2) + b^(2) -c^(2)))/(abc))`
`= (b^(2) + c^(2) -a^(2))/(2a^(2))`
`= (2a^(2) -a^(2))/(2a^(2))`
`= (1)/(2)`
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