How do you do this? Is is just trig division or more?

Question

2cos^2(x)-1 divided by sin(2x) =1

Thanks for direction and steps!

Answer 1

This requires some rearranging using trigonometry:

cos^2(x) = (1+ cos(x))/2

so 2cos^2(x) -1 = cos(2x)


so cos(2x) / sin(2x) = tan (2x)

so tan(2x) = 1

since tan (x) is usually = 1 when x = 45 degrees
on a scale of 0 to 90 degrees or pi/4 on a scale
of 0 to pi/2, x is likely 22.5 degrees or pi/8 depending on what the question is asking.

Answer 2

The numerator of your fraction is
cos 2x. (Verify by expanding cos(x+x) and then
substituting sin^2x = 1 - cos^2x)
So cos 2x/sin 2x = 1.
So sin 2x/cos 2x = 1.
tan 2x = 1
There are 2 angles between 0 and 360(degrees)
that work: 2x = 45 or 225
so x = 22.5 or 112.5(degrees).

Answer 3

shouldnt u do ur own hmwrk......t_t T_T