let give A= ( cosθ −sinθ )
( sinθ cosθ )
1) calculate^t A. A .prove that A is inversible and find
A^(−1)
2) find A^n for n∈ N
3) developp (A +A^(−1) )^n then prove that
2^n cos^n θ = Σ_(k=0) ^n C_n ^k (n−2k)θ and
Σ_(k=0) ^n C_n ^n sin(n−2k)θ =0 .
suppose one of the side of any
box that can be carried onto an
airplane must be less than 8m.
Find the maximum value of such
a box if the sum of the three sides
can not exceed 46m.