Question

Answer the question in the picture

Answer 1

• left picture (bottom expression): -cot(x)
• right picture (top expression): tan(x)

Explanation:

A graphing calculator can show you a graph of each expression, which you can compare to the offered choices.

_____

You can make use of the relations ...

... sin(a)+sin(b) = 2sin((a+b)/2)cos((a-b)/2)

... cos(a)+cos(b) = 2cos((a+b)/2)cos((a-b)/2)

... cos(a)-cos(b) = -2sin((a+b)/2)sin((a-b)/2)

Then you have ...

`(cos(2x)-cos(4x))/(sin(2x)+sin(4x))=(2sin(3x)sin(x))/(2sin(3x)cos(x))=(sin(x))/(cos(x))=tan(x)`

and ...

`(cos(2x)+cos(4x))/(sin(2x)-sin(4x))=(2cos(3x)cos(x))/(-2cos(3x)sin(x))=(-cos(x))/(sin(x))=-\cot{x}`