Given, sin x + cos x = a

To find the value of |sin x – cos x|

Consider square of |sin x – cos x|

|sin x – cos x|² = |sin x|² + |cos x|² – 2|sin x| |cos x|

[using the formula (a + b)²= a² + b² +2 ab]

|sin x – cos x|² = |sin x|² + |cos x|² – 2|sin x| |cos x|

= (sin² x + cos² x)–[(sin x + cos x)² –sin² x –cos² x]

= (sin² x + cos² x)–[a² – (sin² x + cos² x) ]

[using the formula sin² x + cos² x = 1]

= 1 – a² + 1

= 2 – a²

|sin x – cos x|² = 2 – a²

Taking square root on both sides.

Hence