Question

If in a $△ABC$, the altitudes from the vertices A, B, C on opposite sides are in HP, then sin A, sin B, sin C are in

• A. HP
• B. Arithmetico-Geometric progression
• C. AP
• D. GP

Answer 1

The correct option is C AP

$\cos (90-B)=\frac{AD}{c}$

$\Rightarrow AD=c\sin B$

Similarly, $AD,BE,CF$ 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 $AP$