Детерминанта

[Гост]

[tex]\begin{array}{|l}sin(x+p), sin(x+q), sin(x+r)\\sin(y+p), sin(y+q), sin(y+r)\\sin(z+p), sin(z+q), sin(z+r) \end{array}[/tex][tex]\begin{array}{|l} \\\\\\\end{array}[/tex]=?

[aifC]

Съкратен запис по метода на Гаус:

[tex]\Delta = \begin{vmatrix}sin\left(x+p\right)&sin\left(x+q\right)&sin\left(x+r\right)\\ \:\:\:\:\:sin\left(y+p\right)&sin\left(y+q\right)&sin\left(y+r\right)\\ \:\:\:\:\:sin\left(z+p\right)&sin\left(z+q\right)&sin\left(z+r\right)\end{vmatrix}[/tex]

[tex]\left|\begin{matrix}
\sin\left(p+x\right) & \sin\left(q+x\right) & \sin\left(r+x\right) \\
0 & \frac{-\cos\left(p-q-x+y\right)+\cos\left(p-q+x-y\right)}{2*\sin\left(p+x\right)} & \frac{-\cos\left(p-r-x+y\right)+\cos\left(p-r+x-y\right)}{2*\sin\left(p+x\right)} \\
0 & 0 & 0
\end{matrix}\right| = 0[/tex]

[Гост]

[tex]\Rightarrow[/tex][tex]\begin{array}{|l} sin x cos p + cos x sin p, sin x cos q + cos x sin q, sin x cos r + cos x sin r\\ sin y cos p + cos y sin p, sin y cos q + cos y sin q, sin y cos r + cos y sin r\\ sin z cos p + cos z sin p, sin z cos q + cos z sin q, sin z cos r + cos z sin r \end{array}[/tex][tex]\begin{array}{|l} \\ \\ \\ \end{array}[/tex][tex]\Rightarrow[/tex][tex]\begin{array}{|l} sinx, cosx, 0 \\ siny, cosy, 0\\sinz, cosz, 0 \end{array}[/tex][tex]\begin{array}{|l} \\ \\ \\ \end{array}[/tex].[tex]\begin{array}{|l} cosp, cosq, cosr \\ sinp, sinq, sinr\\0, 0, 0 \end{array}[/tex][tex]\begin{array}{|l} \\ \\ \\ \end{array}[/tex]=0.0=0

[Гост]

Значи джичирминантътъ е нуъ, ама задачата на седмицата кой шъ реши?