Question

2A=[ matrix cos theta+ sqrt 3 sin theta&sin theta- sqrt 3 cos theta\\ sqrt 3 cos theta-sin theta&cos theta+ sqrt 3 sin theta matrix ],B=( matrix 1&1\\ 0&1 matrix ) then A ^ T * P ^ 2021 * A is equal to (a)[ matrix 1&2021\\ 0&1 matrix ); (c)( matrix 2021&2021\\ 0&2021 matrix ); (b)( matrix 1&0\\ 2021&1 matrix ); (d)( matrix 2021&0\\ 2021&2021 matrix ) and P=ABA^ prime ,

Answer 1

Step-by-step explanation:

cosθcosϕ+sinθsinϕ=cos(θ−ϕ)

[cos2θcosθsinθcosθsinθsin2θ][cos2ϕcosϕsinϕcosϕsinϕsin2ϕ]

=[cosθcosϕ(cosθcosϕ+sinθsinϕ)sinθcosϕ(cosθcosϕ+sinθsinϕ)cosθsinϕ(cosθcosϕ+sinθsinϕ)sinθsinϕ(cosθcosϕ+sinθsinϕ)]

=[cosθcosϕcos(θ−ϕ)sinθcosϕcos(θ−ϕ)cosθsinϕcos(θ−ϕ)sinθsinϕcos(θ−ϕ)]

Givenθ−ϕ=(2n+1)2π⇒cos(θ−ϕ)=0

therefore [cosθcosϕcos(θ−ϕ)sinθcosϕcos(θ−ϕ)