Gah: Trigonometry

I've been doing some trigonomtry homework and I've nearly got it done.  All I need done are these three problems... but I can't figure it out...

HAAAAAAAAAAALP!

I need to be able to solve the problems and understand them so working it out is appreciated.

1) 1+sin(theta)/cos(theta) + cos(theta)/1+sin(theta) = 2sec(theta)
2) sin(theta)/1-cot(theta) - cos(theta)/tan(theta)-1 = sin(theta) + cos(theta)
3) (3cos(theta) - 4sin(theta))(squared) + (4cos(theta) + 3cos(theta))(squared) = 25

[3cos(θ) - 4sin(θ)]² + [4cos(θ) + 3cos(θ)]² != 25

[3cos(θ) - 4sin(θ)]² + [4cos(θ) + 3sin(θ)]² = 25

1. Expand
[indent]9cos²(θ) - 24sin(θ)cos(θ) + 16sin²(θ) + 16cos²(θ) - 24sin(θ)cos(θ) + 9sin²(θ) = 25[/indent]
2. Cancel
[indent]9cos²(θ) + 16sin²(θ) + 16cos²(θ) + 9sin²(θ) = 25[/indent]
3. Factor
[indent]9[sin²(θ) + cos²(θ)] + 16[sin²(θ) + cos²(θ)] = 25[/indent]
4. sin²(θ) + cos²(θ) = 1
[indent]9 + 16 = 25[/indent]