Question

$ln\Delta ABC,If\frac{SinA}{SinC}=\frac{Sin(A-B)}{Sin(B-C)}$ then $a^2,b^2,c^2$ are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. A.G.P.

Answer 1

The correct option is A A.P.

$2\sin A\sin (B-C)=2\sin (A-B)\sin C$
$\cos (A-B+C)-\cos (A+B-C)=\cos (A-B-C)-\cos (A-B+C)$
$2\cos (A+C-B)=\cos (A-(B+C))+\cos (A+B-C)$
$2\cos 2B=\cos 2A+\cos 2C$
$2-4{\sin }^{2}B=1-2{\sin }^{2}A+1-2{\sin }^{2}C$
$2{\sin }^{2}B={\sin }^{2}A+{\sin }^{2}C$
$2b^2=a^2+c^2$
$\therefore a^2,b^2,c^{2}areinA.P.$