`(1-tan 2^0 cot 62^0)/( tan 152^0-cot 88^o) (a)`sqrt3` (b)-`sqrt3 `(c) `sqrt2-1` (d)`1-sqrt2`

Options

A. `sqrt(3)`
B. `-sqrt(3)`
C. `sqrt(2)-1`
D. `1-sqrt(2)`

Answer

B

Explanation

L`=(1-tan2^(@)cot62^(@))/(tan152^(@)-cot88^(@))=(1-tan2^(@)cot(90-28)^(@))/(tan(180-28)^(@)-cot(90-2)^(@))`
`rArrL=(1-tan2^(@)tan28^())/(-tan28^(@)-tan2^(@))=-[(1-tan2^(@)tan28^(@))/(tan2^(@)+tan28^(@))]`
`rArrL=(1)/(tan(2+28)^(@))=-(1)/(tan30^(@))=-sqrt(3)`
`[becausetan(A+B)=(tanA+tanB)/(1-tanAtanB)]`