An algebra problem by Nischay Singh

Algebra Level 3

Find the value of the expression below:

$\log(\tan(1^\circ)) \times \log(\tan(2^\circ)) \times \log(\tan(3^\circ)) \times \ldots \times \log(\tan(88^\circ)) \times \log(\tan(89^\circ))$

2 solutions

A Former Brilliant Member
Dec 29, 2017

In the series, we get log (tan $(45^{o})$ ) as a term.

We know that tan $(45^{o})$ = 1.

So we get log (1), and we know that log (1) = 0, thus the product series totals to zero.

Nischay Singh
Dec 10, 2017

In the product series the term "log(tan45)" makes the whole product = 0 (Since Tan45 = 1 and log1=0)