1. (5⁴)²*25/5⁹=5⁸*5²/5⁹=5¹⁰/5⁹=5.
2.
а) 9а-а³=а(3²-а²)=а(3-а)(3+а).
б) 15х²у-20ху²=5ху(3х-4у).
По формуле приведения sin (π/2 + 5x) = cos 5x
√2 · cos 2x · cos 5x - cos 2x = 0
cos 2x · (√2 · cos 5x - 1) = 0
cos 2x = 0 или √2 · cos 5x - 1 = 0
2x = π/2 + πn cos 5x = 1/√2
x = π/4 + πn/2 5x = arccos (1/√2) + 2πk или 5x = - arccos (1/√2) + 2πm
5x = π/4 + 2πk 5x = - π/4 + 2πm
x = π/20 + 2πk/5 x = - π/20 + 2πm/5
F`(x)=-sinx
f`(π/2)=-sinπ/2=-1