1) 10^(sinx)=2^(sinx)*5^(-cosx)
10^(sinx)=5^(-cosx)
2^(sinx)
5^(sinx)=5^(-cosx)
sinx = -cosx
sinx = -cosx
cosx cosx
tgx = -1
x= -π/4 + πn, n∈Z
На отрезке [-5π/2; -π]:
- 5π/2 ≤ -π/4+πn ≤ -π
-5π + π ≤ πn ≤ -π + π
2 4 4
- 9π ≤ πn ≤ - 3π
4 4
-2.25 ≤ n ≤ -0.75
n= -2 x= -π/4 - 2π = -9π/4
n= -1 x= -π/4 - π = -5π/4
Ответ: -9π/4; -5π/4.