IN triangle ABC ,angle A is twice the angle B .show that aXa=b(b+c),where a,b,c are sides opposite to angleA,B,C respectively
 

Asked by satishsingh881 | 22nd Sep, 2014, 11:20: PM

Expert Answer:

T h e space a b o v e space s u m space i s space t o space b e space s o l v e d space b y space u sin g space sin e space r u l e L e t space angle B equals x comma space angle A equals 2 x comma space angle C equals 180 degree minus 3 x fraction numerator a over denominator sin space A end fraction equals fraction numerator b over denominator sin space B end fraction equals fraction numerator c over denominator sin space C end fraction o r comma space fraction numerator a over denominator sin space 2 x end fraction equals fraction numerator b over denominator sin space x end fraction equals fraction numerator c over denominator sin left parenthesis 180 minus 3 x right parenthesis end fraction o r comma fraction numerator a over denominator 2 sin space x. cos space x end fraction equals fraction numerator b over denominator sin space x end fraction equals fraction numerator c over denominator sin space 3 x end fraction o r comma fraction numerator a over denominator 2 sin space x. cos space x end fraction equals fraction numerator b over denominator sin space x end fraction equals fraction numerator c over denominator 3 sin space x minus 4 sin cubed x end fraction o r comma fraction numerator a over denominator 2 cos space x end fraction equals b equals fraction numerator c over denominator 3 minus 4 sin squared x end fraction space left square bracket M u l t i p l y i n g space b y space sin space x space o n space a l l space t h e space t h r e e space t e r m s right square bracket space l e t space fraction numerator a over denominator 2 cos space x end fraction equals b o r comma space cos space x equals fraction numerator a over denominator 2 b end fraction............. left parenthesis i right parenthesis l e t space b equals fraction numerator c over denominator 3 minus 4 sin squared x end fraction o r comma space 3 minus 4 sin squared x equals c over b o r comma space 3 minus 4 left parenthesis 1 minus cos squared x right parenthesis equals c over b o r comma space 3 minus 4 plus 4 space cos squared x equals c over b o r comma space 4 space cos squared x equals c over b plus 1 o r comma space cos squared x equals fraction numerator c plus b over denominator 4 b end fraction S u b s t i t u t i n g space cos space x space i n space t h e space a b o v e space e q u a t i o n comma o r comma space fraction numerator a squared over denominator 4 b squared end fraction equals fraction numerator c plus b over denominator 4 b end fraction o r comma space a squared over b equals c plus b space space space space space space space left square bracket space because b not equal to 0 right square bracket o r comma space a squared equals b left parenthesis b plus c right parenthesis

Answered by Prasenjit Paul | 23rd Sep, 2014, 10:26: AM