Question

Solve the equation √3 sin x - cos x = √2

Answer 1

hope this helps you

Answer 2

 x = 75°  or 165°   if √3 sin x - cos x = √2

Step-by-step explanation:

√3 sin x - cos x = √2

Dividing by 2 on both sides

=> (√3 /2 ) sin x -  cos x (1/2)  = √2/2

using Cos30° = √3 /2  & Sin30° = 1/2

=>  sin x Cos30°  - cos x Sin30° = 1/√2

Using Sin(A - B) = sinACosB - CosASinB

& sin45° = 1/√2

=> Sin(x - 30°) = Sin45° or Sin135°

=> x - 30° = 45°  or 135°

=> x = 75° or 165°

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