The cotangent of the angles \(\fracπ3\), \(\fracπ4\) and \(\frac�

1.	The cotangent of the angles \(\fracπ3\), \(\fracπ4\) and \(\fracπ6\) are in(a) A.P (b) G.P. (c) H.P. (d) None of these
Answer» (b) G.P cot \(\fracπ3\) = cot 60° = \(\frac{1}{\sqrt3}\), + cot \(\fracπ4\) = cot 45° = 1, cot \(\fracπ6\) = cot 30° = √3 We can see that \(\bigg(cot \fracπ3\bigg).\bigg(cot\bigg(\frac{π}{6}\bigg)\bigg)=\frac{1}{\sqrt3}.\sqrt3=1=\bigg(cot\frac{π}{4}\bigg)^2\) ∴ cot \(\fracπ3\), cot \(\fracπ4\), cot \(\fracπ6\) are in G.P

The cotangent of the angles \(\fracπ3\), \(\fracπ4\) and \(\fracπ6\) are in(a) A.P (b) G.P. (c) H.P. (d) None of these

Answer»

(b) G.P

cot \(\fracπ3\) = cot 60° = \(\frac{1}{\sqrt3}\), + cot \(\fracπ4\) = cot 45° = 1, cot \(\fracπ6\) = cot 30° = √3

We can see that

\(\bigg(cot \fracπ3\bigg).\bigg(cot\bigg(\frac{π}{6}\bigg)\bigg)=\frac{1}{\sqrt3}.\sqrt3=1=\bigg(cot\frac{π}{4}\bigg)^2\)

∴ cot \(\fracπ3\), cot \(\fracπ4\), cot \(\fracπ6\) are in G.P