Solving Trig Related Physics Problem: Step by Step Guide

[rockytriton]

I'm trying to solve a physics problem with some trig in it. I'm looking at a solution but I'm not understanding where it gets from one step to another.

I understand it up to this point:

19.6m + 800m * cos(Z)^2 = 2,000m * sqr(1 - cos(Z)^2) * cos(Z)

But I don't understand how they get from that to:

384m^2 + 31,360m^2 * cos(Z)^2 + 640,000m^2 * cos(Z)^4 =
4,000,000m^2 * cos(Z)^2 - 4,000,000m^2 * cos(Z)^4

Is this some kind of crazy trig trick that I don't know about?

 

[metacristi]

I'm trying to solve a physics problem with some trig in it. I'm looking at a solution but I'm not understanding where it gets from one step to another.

I understand it up to this point:

19.6m + 800m * cos(Z)^2 = 2,000m * sqr(1 - cos(Z)^2) * cos(Z)

But I don't understand how they get from that to:

384m^2 + 31,360m^2 * cos(Z)^2 + 640,000m^2 * cos(Z)^4 =
4,000,000m^2 * cos(Z)^2 - 4,000,000m^2 * cos(Z)^4

Is this some kind of crazy trig trick that I don't know about?

Raise both sides of the equation to the second power and here you are (approximately, should have been 384.16m^2).