Question

In the given figure, ΔABC is right angled at B.AD divides BC in the ratio 1 : 2. Find
(i) `("tan"∠"BAC")/("tan"∠"BAD")` (ii) `("cot"∠"BAC")/("cot"∠"BAD")`

Answer 1

we are given that BD : DC = 1 : 2 as AD divides BC in the ratio 1 : 2. i.e BD = x,DC = 2x ⇒ BC = 3x

(i) `("tan"∠"BAC")/("tan"∠"BAD")`

= `("BC"/"AB")/("BD"/"AB")`

= `"BC"/"BD"`

= `(3x)/x`
= 3

(ii) `("cot"∠"BAC")/("cot"∠"BAD")`

= `("AB"/"BC")/("AB"/"BD")`

= `"BD"/"BC"`

= `x/(3x)`

= `(1)/(3)`.