A) HP
B) arithoietic-geometric progression
C) AP
D) GP
Correct Answer: C
Solution :
In \[\Delta BDA,\]\[\cos ({{90}^{o}}-B)=\frac{AD}{c}\] \[\Rightarrow \] \[AD=c\sin B\] Similarly, \[BE=a\sin C\]and \[CF=b\sin A\] Since, \[AD,BE,CF\]are in HP. \[\therefore \] \[c\sin B,a\sin C,b\sin A\]are in HP. \[\Rightarrow \frac{1}{\sin C\sin B},\frac{1}{\sin A\sin C},\frac{1}{\sin B\sin A}\]are in AP \[\Rightarrow \] \[\sin A,\sin B,\sin C\]are in AP. (multiply by \[\text{sinA sinB sinC}\])You need to login to perform this action.
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