सिद्ध कीजिए कि [(cos^2α cosαsinα),(cosαsinα sin^2α)][(cos^2β cosβsinβ),(cosβsinβ sin^2β)]जबकि α – β = (2m – 1)π/2, m∈N

Question

सिद्ध कीजिए कि  \(\begin{bmatrix} cos^2α &cosα\,sinα \\[0.3em] cosα\,sinα&\,sin^2α \\[0.3em] \end{bmatrix}\)  \(\begin{bmatrix} cos^2β&cosβ\,sinβ \\[0.3em] cosβ\,sinβ&\,sin^2β \\[0.3em] \end{bmatrix}\)= 0 जबकि α – β = (2m – 1)π/2, m∈N

Answer 1

= cos (α – β) [cos α cos β sin α sin β – cos α cos β sin α sin β]

= cos (α – β) x 0

= 0

= R.H.S.