Correct Answer - Option 2 : p
2(2 - p
2)
Concept:
sin2 x + cos2 x = 1
sin 2x = 2 sin x cos x
cos 2x = cos2 x - sin2 x
Calculation:
Given: sin x - cos x = p
By squaring both the sides, we get
⇒ sin2 x + cos2 x - 2 sin x cos x = (p)2
As we know that, sin2 x + cos2 x = 1 and sin 2x = 2 sin x cos x
⇒ 1 - sin 2x = p2
⇒ sin 2x = 1 - p2
As we know that, sin2 x + cos2 x = 1
∴ sin2 2x + cos2 2x = 1
⇒ cos2 2x = 1 – sin2 2x
= 1 – (1 - p2)2
= 1 - 1 - p4 + 2p2
= p2(2 - p2)