Expert: Scott A Wilson - 3/10/2011

Question
QUESTION: if log of sinx with base cosx + log of cosx with base sinx =2   
then find tanx

ANSWER: Looking at the problem, I can see that sin(pi/2) = cos(pi/2),
so the log of x base x is 1, and so 1 + 1 = 2, so the answer is pi/2.



---------- FOLLOW-UP ----------

QUESTION: please give some more explanation

Answer
I'm sorry about that - what I really meant was π/4.
That is, sin(π/4) = cos(π/4) = 1/√2.

The way I got it was to note that the simplest way to do it was if both expressions were 1.
This means that if the number and the base are the same, the log is 1.
If the angle is π/4, then that is where cos x = sin x.