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Question: If the area of triangle ABC is a<sup>2</sup> – (b –c)<sup>2</sup>, then tan A equals to-...

If the area of triangle ABC is a2 – (b –c)2, then tan A equals to-

A

–8/15

B

15/16

C

8/15

D

15/8

Answer

8/15

Explanation

Solution

As given s(s−a)(s−b)(s−c)\sqrt { s ( s - a ) ( s - b ) ( s - c ) }

= (a + b –c) (a –b + c) = (2s –2c) (2s –2b)

⇒ s(s−a)(s−b)(s−c)\sqrt { \frac { s ( s - a ) } { ( s - b ) ( s - c ) } }= 4 ⇒ cot A2\frac { \mathrm { A } } { 2 } = 4

⇒ tan A2\frac { \mathrm { A } } { 2 } = 14\frac { 1 } { 4 } ⇒ tan A = 2tan⁡A/21−tan⁡2 A/2\frac { 2 \tan \mathrm { A } / 2 } { 1 - \tan ^ { 2 } \mathrm {~A} / 2 } = 815\frac { 8 } { 15 }