Sir how to find its domain and range.please solve it .Its answer is 2nπ-π/2‹x‹2nπ+π/2

Here what we want is sin(cosx) >0

Value of cosx(let m=cosx) oscillates from -1 to 1

I.e. -1 ≤m≤1

sinm ≥ 0 for 0 ≤m≤ π/2 or 0≤m≤ 1….(1)

sinm

For sin(cosx) >0 we select 1st option

I.e 0≤ cosx≤1

x € [(2 n+1)π/2, (2 n+3)π/2] where n € odd integer.