# Question #24816

Feb 23, 2017

The given expression will be equal to Zero

$5 , 9 , 13 , \ldots . .$ this is in AP having first term 5 and common difference 4.

Let 45 be its nth term.

So $5 + \left(n - 1\right) \cdot 4 = 45$

$\implies n - 1 = \frac{45 - 5}{4} = 10$

$\implies n = 10 + 1 = 11$

So 11 th term of the AP is 45.

Hence 11 th factor of the given product will be

$\log \tan 45 = \log 1 = 0$

So value of the given expression will be Zero.