Question

Express √3 cosx + sinx in the form of R sin(x+infinity)​

Answer 1

Answer:

Step-by-step explanation:

cosx+3–√sinx=2cos(x−60∘)=2–√

So, cos(x−60∘)=12√=cos45∘

⟹x−60∘=n360∘±45∘ where n is any integer

Taking ′+′ sign, x−60∘=n360∘+45∘⟹x=n360∘+105∘

If 0≤x≤360∘,0≤n360∘+105∘≤360∘⟹n=0

Taking ′−′ sign, x−60∘=n360∘−45∘⟹x=n360∘+15∘

If 0≤x≤360∘,0≤n360∘+15∘≤360∘⟹n=0

So, x=15∘,105∘