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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")`
Solution
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)`.
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