Question

The minimum
value of cos θ + sin θ is _____
please answer fast its urgent ​

Answer 1

Answer:

$\sqrt{2} and - \sqrt{2}$

Step-by-step explanation:

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

Now,

f(θ)=2–√(12√sinθ+12√cosθ)=2–√(cosπ4sinθ+sinπ4cosθ)=2–√sin(θ+π4)

f(θ) is minimum when sin is minimum. The minimum value of sin is -1 which occurs at −π2 . Therefore, θ+π4=−π2 , giving θ=−3π4 and the minimum value is −2–√ .