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Question
In any ∆ABC, prove that the area ∆ = `("b"^2 + "c"^2 - "a"^2)/(4 cot "A")`
Solution
Area of ∆ABC is ∆ = `1/2` bc = sin A
Using cosine formula
cos A = `("b"^2 + "c"^2 - "a"^2)/(2"bc")`
bc = `("b"^2 + "c"^2 - "a"^2)/(2cos"A")`
∆ = `1/2 xx ("b"^2 + "c"^2 - "a"^2)/(2cos"A") xx sin "A"`
= `1/4 * ("b"^2 + "c"^2 - "a"^2) tan "A"`
∆ = `("b"^2 + "c"^2 - "a"^2)/(4 cot "A")`
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