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

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

A

– 43\frac { 4 } { 3 }

B

43\frac { 4 } { 3 }

C

815\frac { 8 } { 15 }

D

415\frac { 4 } { 15 }

Answer

43\frac { 4 } { 3 }

Explanation

Solution

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 ) } }

tan A2\frac { \mathrm { A } } { 2 } = 12\frac { 1 } { 2 }

∴ tan A = 2×121−14\frac { 2 \times \frac { 1 } { 2 } } { 1 - \frac { 1 } { 4 } }= 43\frac { 4 } { 3 }