Question

How do you use the half angle formulas to simplify the expression `-sqrt((1-cos8x)/(1+cos8x))`?

Answer 1

`-|tan (4x)|` See Socratic graph for both.

Explanation:

The expression is

`-sqrt(sin^2(4x)/cos^2(4x))`

#=-|tan (4x)|, using sqrt(a^2)=|a|, by convention.practice/definition.
graph{-sqrt((1-cos (8x))/(1+cos(8x)) [-0.8765, 0.8765, -0.438, 0.4385]}

graph{-|tan(4x)| [-0.8765, 0.8765, -0.438, 0.4385]}