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Question: If D = a<sup>2</sup> – (b – c)<sup>2</sup>, where D is the area of triangle ABC, then tan A is equa...

If D = a2 – (b – c)2, where D is the area of triangle ABC, then

tan A is equal to-

A

1516\frac { 15 } { 16 }

B

815\frac { 8 } { 15 }

C

817\frac { 8 } { 17 }

D

12\frac { 1 } { 2 }

Answer

815\frac { 8 } { 15 }

Explanation

Solution

D = a2 – (b – c)2

D = [a – (b – c)] [a + (b – c)]

D = (a + c – b) (a + b – c)

D = (2s –2b) (2s –2c)

s(s−a)(s−b)(s−c)\sqrt { s ( s - a ) ( s - b ) ( s - c ) } = 4 (s – b) (s – c)

= 4 (s−b)(s−c)\sqrt { ( s - b ) ( s - c ) }

̃= 14\frac { 1 } { 4 }

̃ tan = 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 }

tan A = 2(1/4)1−1/16\frac { 2 ( 1 / 4 ) } { 1 - 1 / 16 }= 815\frac { 8 } { 15 }