It's a question from resonance booklet... Plz may I know the answer??

continuation for the above sum;-)=-Sin^2?cos^2?[cos^(n-4)?+sin^(n-4)?]=-sin^2?cos^2?[P(n-4)]2) Q(n-2) =cos^n?/cos^2?-sin^n?/sin^2?Q(n)-Q(n-2)=cos^n?[1-1/cos^2?]+sin^n?[1/sin^2?-1]==cos^n?[-sin^2?/cos^2?]+sin^n?[cos^?/sin^2?]=sin^2?cos^2?[-cos^(n-4)?+sin^(n-4)?]=-sin^2?cos^2?[Q(n-4)](3) P(4)=cos^4?+sin^4? =[cos^2?+sin^2?]^2-2sin^2?cos^2? ==1-2sin^2?cos^2?(4). Q(4)=cos^4?-sin^4? =[Cos^2?+sin^2?].[cos^2?-sin^2?] =cos^2?-sin^2?..

P(n-2)=cos^(n-2)?+sin^(n-2)? =cos^(n)?/cos^2?+sin^(n)?/sin^2?P(n)-P(n-2)=cos^n?[1-1/cos^2?]+sin^n?[1-1/sin^2?]==Cos^n?[-sin^2?/cos^2?]+sin^n?[-cos^2?/sin^2?]==Sin^2?.cos^2?[-cos^(n-4)?-sin^(n-4)?]==Sin^2?cos^2?