Question

the mum value of (cos theeta - sin theeta ) is
1)0
2)1
3)-1
4)-√2​

Answer 1

Answer:

_√2

Step-by-step explanation:

Let f(θ)=sinθ+cosθ, and although unimportant, let Dom(f)=[−π,π] .

Now,

f(θ)=√2(sinθ/√2+√cosθ/√2)=√2(cosπ4sinθ+sinπ4cosθ)=√2sin(θ+π/4)

f(θ) is minimum when sin is minimum. The minimum value of sin is -1 which occurs at −π/2. Therefore, θ+π/4=−π/2, giving θ=−3π/4 and the minimum value is −√2