Fill in the blank

Given that, sin x + cos x = a

Squaring both sides, we get

(sin x + cos x)² = a²

⇒ sin²x + cos²x + 2sin x cos x = a²

⇒ 1 + 2sin x cos x = a²

(i) sin⁶ x + cos⁶x = (sin²x)³ + (cos²x)³

= (sin²x+ cos²x)³ -3 sin²x cos²x(sin²x+ cos²x)

(ii) |sin x – cos x| =

|sin x – cos x|² = sin²x + cos²x - 2sin x cos x

=1-(a² -1)

= 1-a²+1 = 2- a²

⇒ |sin x – cos x| =