left|begin{array}{ccc}cos alpha cos beta & co | vedclass

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(C) ધારો કે $\Delta = \left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \ -\sin \beta & \cos \beta & 0 \ \sin \

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(C) ધારો કે $\Delta = \left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \ -\sin \beta & \cos \beta & 0 \ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}ight|$.ત્રીજા સ્તંભ $(C_3)$ ની સાપેક્ષ વિસ્તરણ કરતા:$\Delta = -\sin \alpha \left( (- \sin \beta)(\sin \alpha \sin \beta) - (\cos \beta)(\sin \alpha \cos \beta) ight) + \cos \alpha \left( (\cos \alpha \cos \beta)(\cos \beta) - (\cos \alpha \sin \beta)(-\sin \beta) ight)$$\Delta = -\sin \alpha \left( -\sin \alpha \sin^2 \beta - \sin \alpha \cos^2 \beta ight) + \cos \alpha \left( \cos \alpha \cos^2 \beta + \cos \alpha \sin^2 \beta ight)$$\Delta = -\sin \alpha [-\sin \alpha (\sin^2 \beta + \cos^2 \beta)] + \cos \alpha [\cos \alpha (\cos^2 \beta + \sin^2 \beta)]$કારણ કે $\sin^2 \beta + \cos^2 \beta = 1$,તેથી:$\Delta = -\sin \alpha [-\sin \alpha (1)] + \cos \alpha [\cos \alpha (1)]$$\Delta = \sin^2 \alpha + \cos^2 \alpha$$\Delta = 1$.

$\left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \\ -\sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}\right|$ ની કિંમત શોધો.

Similar Questions

સમીકરણ $\left| \begin{matrix} 1+x & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+x \end{matrix} \right| = 0$ ના બીજ કયા છે?

જો $\left| \begin{array}{ccc} a & b & c \\ b & c & a \\ c & a & b \end{array} \right| = k(a + b + c)(a^2 + b^2 + c^2 - bc - ca - ab)$ હોય,તો $k =$

$\left| {\begin{array}{ccc} {1^2} & {2^2} & {3^2} \\ {2^2} & {3^2} & {4^2} \\ {3^2} & {4^2} & {5^2} \end{array}} \right|$ નું મૂલ્ય શોધો.

જો સમીકરણોની સિસ્ટમ $2x + 3y - z = 0$,$x + ky - 2z = 0$ અને $2x - y + z = 0$ નો ઉકેલ $(x, y, z)$ શૂન્યેતર (non-trivial) હોય,તો $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k$ ની કિંમત શોધો.

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