Statement I: Let D1=1cosαcosβcosα1cosγcosβcosγ1=1−cos2α−cos2β−cos2γ+2cosαcosβcosγ.
D2=0cosαcosβcosα0cosγcosβcosγ0=2cosαcosβcosγ.
D1=D2⇒1−cos2α−cos2β−cos2γ=0⇒cos2α+cos2β+cos2γ=1=23. Statement I is false.
Statement II: Evaluate by substituting x=0: determinant =−12, so q=−12.
At x=1: determinant =12, so p+q=12⇒p=24.
p2=576 and 196q2=196×144=28224. Since p2=196q2, Statement II is false.
Both statements are false.