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Question: In ∆ABC if 2∆ = a<sup>2</sup> – (b – c )<sup>2</sup> then value of tan A equals...

In ∆ABC if 2∆ = a2 – (b – c )2 then value of tan A equals

A

–43\frac{–4}{3}

B

43\frac{4}{3}

C

815\frac{8}{15}

D

None

Answer

43\frac{4}{3}

Explanation

Solution

Q 2∆ = (a – b + c) (a + b – c)

2∆ = 4 (s – b) (s – c)

2 = s(s–a)(s–b)(s–c)\sqrt{\frac{s(s–a)}{(s–b)(s–c)}}⇒ tanA2\frac{A}{2} = 12\frac{1}{2}

⇒ tanA = 2.121–14\frac{2.\frac{1}{2}}{1–\frac{1}{4}} = 43\frac{4}{3}