Question

Find the maximum and minimum values of sin 2x - cos 2x

Answer 1

Please see the attachment

Answer 2

Answer:

Min Value = - √2   & Max Value = √2

Step-by-step explanation:

Let say  A  = sin 2x - cos 2x

Squaring both sides

=> A² = (sin 2x - cos 2x )²

=> A² = Sin²2x + Cos²2x - 2Sin2xCos2x

=> A² = 1 - Sin4x

-1 ≤ Sin4x ≤ 1

Sin4x = -1

=> A² = 1 - (-1) = 2  => A = ±√2

Sin4x = 1

=> A² = 0 => A  = 0

Min Value = - √2   & Max Value = √2