1) Since sin²(5a) + cos²(5a) = 1, we can simplify the expression as follows:

2sin²(5a) + 2cos²(5a)
= 2(1 - cos²(5a)) + 2cos²(5a) [Using the Pythagorean identity sin²(θ) = 1 - cos²(θ)]
= 2 - 2cos²(5a) + 2cos²(5a)
= 2

Therefore, the expression simplifies to 2.

2) Using the trigonometric identity sin(2θ) = 2sin(θ)cos(θ) and ctg(θ) = 1/tan(θ), we have:

sin(2Ф) ctg(2Ф) = 2sin(Ф)cos(Ф) 1/tan(2Ф)
= 2sin(Ф)cos(Ф) 1/(2tan(Ф)/(1 - tan²(Ф))) [Using the formula tan(2θ) = 2tan(θ)/(1 - tan²(θ))]
= 2sin(Ф)cos(Ф) * (1 - tan²(Ф))/(2tan(Ф))
= sin(2Ф)

Therefore, the expression simplifies to sin(2Ф).