Spherical Coordinates (need work double checked please)

[clickcaptain]

Could someone double check to make sure my calculations are all done right? I've done this problem several times and gotten the same answer but the online submission says its wrong so I need someone else to check my work. thanks!

Homework Statement

Homework Equations

x = ρ sin(Φ) cos(θ)
y = ρ sin(Φ) sin(θ)
z = p cos(Φ)

The Attempt at a Solution

4z² = x²+y²

4p ²cos²(Φ) = ρ ²sin²(Φ) cos²(θ) + ρ ²sin²(Φ) sin²(θ)

cos²(Φ) = (ρ ²sin²(Φ) cos²(θ) + ρ ²sin²(Φ) sin²(θ))/ (ρ ² *4)

***(ρ²'s cancel right?)****

so I'm left with for an answer

cos²(Φ) = (sin²(Φ) cos²(θ) + sin²(Φ) sin²(θ))/ 4)

 

[HallsofIvy]

How about using the fact that $sin^2(\theta)+ cos^2(\theta)= 1$?!

 

[clickcaptain]

I didn't think you could use that when your are talking about two different angles (Φ and θ)?

I tried it anyway though and its a no go...

 

[Defennder]

What HallsOfIvy meant was that you should factor out sin²(Φ) in the numerator of your final expression and apply that trigo identity. That will simplify your final answer.