if-D-determinant-1-3sin-1-sin-1-3cos-1-sin-1-the-maxi-mum-value-of-D-is-

Question Number 10776 by j.masanja06@gmail.com last updated on 24/Feb/17

if D = | \begin{matrix} 1 & 3 \sin θ & 1 \\ \sin θ & 1 & 3 \cos θ \\ 1 & \sin θ & 1 \end{matrix} | the maxi

mum value of D is ?

Answered by sandy_suhendra last updated on 24/Feb/17

D = 1 + 9 \sin θ \cos θ + \sin θ \cos θ - (1 + 3 \sin θ \cos θ + 3 \sin θ \cos θ)

= 4 \sin θ \cos θ = 2 \sin 2 θ

because maximum for \sin 2 θ = 1

so D maximum = 2