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Derivative of Standard Functions

tan10π/3, tan...

Question

$tan \frac{10 π}{3}, tan \frac{9 π}{4}, tan \frac{7 π}{6}$ are in

A

AP

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B

GP

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C

HP

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D

none of these

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Solution

The correct option is B GP
we have $tan (\frac{10 π}{3}) = tan (3 π + \frac{π}{3}) = tan (\frac{π}{3}) = \sqrt{3} tan (\frac{9 π}{4}) = tan (2 π + \frac{π}{4}) = tan (\frac{π}{4}) = 1 tan (\frac{7 π}{6}) = tan (π + \frac{π}{6}) = tan (\frac{π}{6}) = \frac{1}{\sqrt{3}}$
thus clearly we can see that ${(tan (\frac{9 π}{4}))}^{2} = tan (\frac{10 π}{3}) tan (\frac{7 π}{6})$
Hence they are in G.P
So the correct option is B.

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