MathematicsThe cotangents of the angles π3, π4, π6are in

The cotangents of the angles $\frac{π}{3}, \frac{π}{4}, \frac{π}{6}$ are in

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

Solution:

The given angles are $\frac{π}{3}, \frac{π}{4}, \frac{π}{6}$

We know that

$c o t (\frac{π}{3}) = \frac{1}{\sqrt{3}}$
$c o t (\frac{π}{4}) = 1$
$c o t (\frac{π}{6}) = \sqrt{3}$

The values $\frac{1}{\sqrt{3}}, 1, \sqrt{3}$ are in Geometric progression with common ratio $\sqrt{3}$

Therefore, cotangents of the angles of $\frac{π}{3}, \frac{π}{4}, \frac{π}{6}$ are in $G . P$

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