25^cos (3 п/2+x) = 5^1-cos2x

Корни на отрезке: [-5 п; - 3 п/2]

5^2cos (3π/2+x) = 5^1-cos2x

2cos (3π/2+x) = 1-cos2x

2sinx=2sin²x

2sin²x-2sinx=0

2sinx (sinx-1) = 0

sinx=0⇒x=πn, n∈z

-5π≤πn≤-3π/2

-5≤n≤-3/2

n=-5⇒x=-5π

n=-4⇒x=-4π

n=-3⇒x=-3π

n=-2⇒x=-2π

sinx=1⇒x=π/2+2πk, k∈z

-5π≤π/2+2πk≤-3π/2

-10≤1+4k≤-2

-11≤4k≤-3

-11/4≤k≤-3/4

k=-2⇒x=π/2-4π=--7π/2

n=-1⇒x=π/2-2π=-3π/2