Question

tan π/3, tan π/4 and tan π/6 are in
1) A.P
2)G.P
3) H.P
4) 1 and 3​

Answer 1

The answer in G.P

I hope it will help you

Answer 2

tan π/3 , tan π/4 and tan π/6 are in G.P

Given :

tan π/3, tan π/4 and tan π/6

To find :

tan π/3, tan π/4 and tan π/6 are in

1) A.P

2) G.P

3) H.P

4) 1 and 3

Concept :

a , b , c are said to be in GP in b² = ac

Solution :

Step 1 of 2 :

Write down the given terms

Here the given terms are tan π/3, tan π/4 and tan π/6

tan π/3 = √3

tan π/4 = 1

tan π/6 = 1/√3

Step 2 of 2 :

Choose the correct option

Let a = tan π/3 , b = tan π/4 and c = tan π/6

Then a = √3 , b = 1 , c = 1/√3

We have

$\displaystyle \sf{ {b}^{2} = {1}^{2} = 1 }$

$\displaystyle \sf{ac = \sqrt{3} \times \frac{1}{ \sqrt{3} } = 1 }$

Thus we have b² = ac

So tan π/3 , tan π/4 and tan π/6 are in G.P

Hence the correct option is 2) G.P