Question

In $\Delta$ $ABC$ the sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively.

If $a,b,c$ are in Geometric Progression then :

• A. ${\cot }^{2}A,{\cot }^{2}B,{\cot }^{2}C$ are in G. P.
• B. $cose{c}^{2}A,cose{c}^{2}B,cose{c}^{2}C$ are in A. P.
• C. $cosecA,cosecB,cosecC$ are in G. P.
• D. none of these

Answer 1

Answer: (C)

$cosecA,cosecB,cosecC$ are in G. P.

From Sine Rule,

$acosecA=bcosecB=ccosecC$

To satisfy the above condition

if $a,b,c$ are in $GP$ then $cosecA,cosecB,cosecC$ have to be in $GP$

Therefore, $C$ is correct