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JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

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If in a Δ  ABC,  2b2=a2+c2\Delta \;ABC,\;2{b^2} = {a^2} + {c^2}, then sin⁡3Bsin⁡B\frac{{\sin 3B}}{{\sin B}} is equal to
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Correct option: D
(c2−a22ca)2{\left( {\frac{{{c^2} - {a^2}}}{{2ca}}} \right)^2}
Option D, (c2−a22ca)2{\left( {\frac{{{c^2} - {a^2}}}{{2ca}}} \right)^2}, is the correct answer because it is derived by using the trigonometric identity for sin⁡3B\sin 3B and the given condition 2b2=a2+c22b^2 = a^2 + c^2 to simplify the expression.

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