Determinanti trigonometrici

Lauryca Dum Dec 16, 2012 11:18 pm

Sa se calculeze determinantii trigonometrici:
$a)\begin{vmatrix} 1&sin^2x&cos^2x \\ 1 & sin^2y & cos^2y\\ 1& sin^2z & cos^2z \end{vmatrix}$
$b)\begin{vmatrix} cos2x&cosx&1 \\ cos2y& cosy & 1\\ cos2z&cosz & 1 \end{vmatrix}$

**Admin** Lun Dec 17, 2012 12:18 am

Sub-punctul a)
$\begin{array}{l} \left| {\begin{array}{*{20}{c}} 1&{si{n^2}x}&{co{s^2}x}\\ 1&{si{n^2}y}&{co{s^2}y}\\ 1&{si{n^2}z}&{co{s^2}z} \end{array}} \right| = \left| {\begin{array}{*{20}{c}} {a + b}&a&b\\ {c + d}&c&d\\ {e + f}&e&f \end{array}} \right|\\ = \left| {\begin{array}{*{20}{c}} a&a&b\\ c&c&d\\ e&e&f \end{array}} \right| + \underbrace {\left| {\begin{array}{*{20}{c}} b&0&0\\ d&0&0\\ f&0&0 \end{array}} \right|}_{ = 0} = 0 + 0 \end{array}$
Sub-punctul b) tema !

Determinanti trigonometrici

Determinanti trigonometrici

Re: Determinanti trigonometrici