In a linear system, an input of 5 sin ωt produces an output

In a linear system, an input of 5 sin ωt produces an output of 10 cos ωt. The output corresponding to input 10 cos ωt will be equal to—

Given
it means the system is differentiator with ω = 2
So with,
ω = 2
= – 10. ω sin ωt
= – 10 × 2. sin ωt
= – 20 sin ωt,