Given: sin x - cos x = p By squaring both the sides, we get ⇒sin2x+cos2x−2sinxcosx=(p)2 As we know that, sin2x+cos2x=1 and sin2x=2sinxcosx ⇒1−sin2x=p2 ⇒sin2x=1−p2 As we know that, sin2x+cos2x=1 ∴sin22x+cos22x=1 ⇒cos22x=1−sin22x =1−(1−p2)2 =1−1−p4+2p2 =p2(2−p2)