Question

Solve this no spam

mind it determind will be A​

Answer 1

Answer:

Solve this no spam

mind it determind will be A

Step-by-step explanation:

A will be 90...

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Answer 2

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• $\\ \: \: \: \left|\begin{array}{cc}\sf cos\:x & \sf\:sin\:x\\\sf\:-\:sin\:x & \sf\:cos\:x\end{array}\right|$

$\;\;\underline{\textbf{\textsf{ To Find:-}}}$

• $\\ \: \: \: \left|\begin{array}{cc}\sf cos\:x & \sf\:sin\:x\\\sf\:-\:sin\:x & \sf\:cos\:x\end{array}\right| = ?$

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Let the determinant be

$\\ \: \dashrightarrow \: A = \left|\begin{array}{cc}\sf cos\:x & \sf\:sin\:x\\\sf\:-\:sin\:x & \sf\:cos\:x\end{array}\right|$

• We know that –

$\\ \: \dashrightarrow \: A = \left|\begin{array}{cc}\sf a_{11} & \sf a_{12}\\\sf\:a_{21} & \sf a_{22}\end{array}\right|$

$\\ \: \dashrightarrow \sf A =a_{11}.a_{22} -a_{21}.a_{12}$

Where,

$\\ \sf \: \: { \huge{.}} \: \: a_{11} = \cos x$

$\\ \sf \: \: { \huge{.}} \: \: a_{12} = \sin x$

$\\ \sf \: \: { \huge{.}} \: \: a_{21} = - \sin x$

$\\ \sf \: \: { \huge{.}} \: \: a_{22} = \cos x$

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$\underline{\:\textsf{ Now, find the value of A :}}$

$\\ \: \dashrightarrow \: A = \left|\begin{array}{cc}\sf cos\:x & \sf\:sin\:x\\\sf\:-\:sin\:x & \sf\:cos\:x\end{array}\right|$

$\\ \\ \dashrightarrow \sf A = ( \cos x).(\cos x) - ( \sin x)( - \sin x)$

$\\ \\ \dashrightarrow \sf A = \cos^{2} x + \sin^{2} x$

$\\ \: \: \: \sf \because \: \: \: \cos^{2} x + \sin^{2} x = 1$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ Value of A is \textbf{1 }}}.$

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