In triangleABC,if A<BY and sin A,sin BY satisfy the equation 
3sin x-4  sin^3 x-k=0 Where(0<k<1)then angle C=?

Asked by Sunil Soni | 7th Dec, 2015, 10:31: PM

Expert Answer:

C o n s i d e r space t h e space e q u a t i o n comma 3 sin x minus 4 sin cubed x minus k equals 0 G i v e n space t h a t space sin A space a n d space sin B space s a t i s f y space t h e space a b o v e space e q u a t i o n. therefore 3 s i n A minus 4 s i n cubed A equals k a n d therefore 3 s i n B minus 4 s i n cubed B equals k W e space k n o w space t h a t space 3 s i n theta minus 4 s i n cubed theta equals sin 3 theta T h u s comma space w e space h a v e comma sin 3 A equals k space a n d space sin 3 B equals k rightwards double arrow sin 3 A equals sin 3 B A l s o space g i v e n space t h a t comma space A less than B rightwards double arrow sin theta equals sin open parentheses 180 degree minus theta close parentheses rightwards double arrow 3 A equals theta space a n d space 3 B equals 180 degree minus theta rightwards double arrow A equals theta over 3 space a n d space B equals fraction numerator 180 degree over denominator 3 end fraction minus theta over 3 rightwards double arrow A equals theta over 3 space a n d space B equals 60 degree minus theta over 3 W e space k n o w space t h a t space angle A plus angle B plus angle C equals 180 degree rightwards double arrow theta over 3 plus 60 degree minus theta over 3 plus angle C equals 180 degree rightwards double arrow 60 degree plus angle C equals 180 degree rightwards double arrow angle C equals 180 degree minus 60 degree rightwards double arrow angle C equals 120 degree

Answered by Vimala Ramamurthy | 8th Dec, 2015, 08:55: AM