Question

Evaluate $\log \left[\right(\tan 2\left)\right(\tan 4\left)\right(\tan 6).....(\tan 88\left)\right]$

• A. $0$
• B. $2$
• C. $1$
• D. Infinity

Answer 1

The correct option is A $0$

We have,

$\log \left[\right(\tan 2\left)\right(\tan 4\left)\right(\tan 6).....(\tan 88\left)\right]$

$=\log \left[\right(\tan 2\left)\right(\tan 4\left)\right(\tan 6).....\tan (90-4\left)\tan \right(90-2\left)\right]$

$=\log \left[\right(\tan 2\left)\right(\tan 4\left)\right(\tan 6).....(\cot 4\left)\right(\cot 2\left)\right]$ $\because \cot x=\tan (90-x)$

$=\log [1\times 1\times \mathrm{1......}\times 1]$ $\because \cot x=\frac{1}{\tan x}$

$=\log \left[1\right]$

$=0$

Hence, this is the answer.