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

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(C) माना कि $\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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$1$

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(C) माना कि $\Delta = \left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \ -\sin \beta & \cos \beta & 0 \ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}ight|$.तीसरे स्तंभ $(C_3)$ के अनुदिश विस्तार करने पर:$\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)]$चूंकि $\sin^2 \beta + \cos^2 \beta = 1$,इसलिए:$\Delta = -\sin \alpha [-\sin \alpha (1)] + \cos \alpha [\cos \alpha (1)]$$\Delta = \sin^2 \alpha + \cos^2 \alpha$$\Delta = 1$.

$\left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \\ -\sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}\right|$ का मान ज्ञात कीजिए।

Similar Questions

समीकरण $\left| \begin{array}{ccc} \cos \theta & \sin \theta & \cos \theta \\ -\sin \theta & \cos \theta & \sin \theta \\ -\cos \theta & -\sin \theta & \cos \theta \end{array} \right| = 0$ का हल क्या है?

$\left| \begin{array}{ccc} 1 & 1 & 1 \\ a & b & c \\ a^3 & b^3 & c^3 \end{array} \right| = $

यदि $a, b, c$ भिन्न धनात्मक वास्तविक संख्याएँ हैं,तो सारणिक $\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|$ का मान क्या है?

मान लीजिए $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{bmatrix}$ और $|2A|^3 = 2^{21}$,जहाँ $\alpha, \beta \in \mathbb{Z}$ है। तो $\alpha$ का एक मान है:

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