AP EAMCET20228 Jul 2022Morning ShiftMathematicsStraight LinesActual
In a triangle ABC ,( b + c ) A 2 =
Options
- Aa A
- Ba ( B-C 2 )
- Ca ( B+C 2 )
- Da ( B-C 2 )
Correct answer
B. a ( B-C 2 )
Step-by-step solution
In ABC ( b + c ) Sin ( A 2 )= ? By Sin rule a Sin A = b Sin A = c Sin C =k a = k A , b = k B , c = k C Now (b+c) ( A 2 )=(K B+K C) Sin ( A 2 )= k ( B + C ) Sin ( A 2 ) aligned & = k [2 ( B + C 2 ) ( B - C 2 ) ] ( A 2 ) & = k [2 ( + A 2 ) ( B - C 2 ) ] ( A 2 ) & = k [2 ( 2 - A 2 ) ( B - C 2 ) ] ( A 2 ) & = k [2 ( A 2 ) ( B - C 2 ) ] ( A 2 ) & = k Sin A ( B - C 2 ) aligned = a ( B - C 2 )