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If tanx+tany=25 and cotx+coty=30 then th...

If `tanx+tany=25` and `cotx+coty=30` then the value of `tan(x+y)` is

A

`100`

B

`150`

C

`250`

D

`200`

Text Solution

Verified by Experts

The correct Answer is:
B
If `tan x + tan y = 25` …………
`tan x + tan y = 25`
`cot x + xot y = 30 i.e. (25)/(tan x tan y) = 30`
`:. tan x tan y = (25)/(30) = (5)/(6)`
`:. tan (x+y) = (tan x + tan y)/(1-tan x tan y) = (15)/(1-(5)/(6)) = 150`
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