Question

The cotangent of the angles π/3,π/4 and π/6 are in what king of progression?
A) AP. B)GP. C)HP. D) No Sequence

Answer 1

cotπ/3, cotπ/4, cotπ/6,

1/√3, 1 , √3,

now here

a2/a1=1/(1/√3) =√3,

a3/a2=√3/1 =√3,

since

a2/a1 = a3/a2,


therefore it will be a G.P

Answer 2

The geven progression "option B) GP" is correct.

Step-by-step explanation:

We have,

$\cot \dfrac{\pi}{3}, \cot \dfrac{\pi}{4}$ and $\cot \dfrac{\pi}{6}$

To chceck what kind of progression = ?

∴ $\cot \dfrac{\pi}{3}, \cot \dfrac{\pi}{4}$ and $\cot \dfrac{\pi}{6}$

⇒ $\cot 60, \cot 45$ and $\cot 30$

⇒ $\dfrac{1}{\sqrt{3}} , 1$ and $\sqrt{3}$

∴= Common ratio(r) $=\dfrac{Second term}{First term} =\dfrac{Third term}{second term}$

$\dfrac{1}{\dfrac{1}{\sqrt{3}}} =\sqrt{3}$ or

$\dfrac{\sqrt{3}}{1}=\sqrt{3}$

The commmon ratios are equal.

The given progression is GP.

Hence, the given progression "option B) GP" is correct.