Left| {,begin{array}{*{20}{c}}{{{sin }^2}x}&{{{cos }^2}x}&1{{{cos }^2}x}&{{{sin }^2}x}&a

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3 and 4 .Determinants and Matrices

easy

$\left| {\,\begin{array}{*{20}{c}}{{{\sin }^2}x}&{{{\cos }^2}x}&1\\{{{\cos }^2}x}&{{{\sin }^2}x}&1\\{ - 10}&{12}&2\end{array}\,} \right| = $

A

$0$

B

$12{\cos ^2}x - 10{\sin ^2}x$

C

$12{\sin ^2}x - 10{\cos ^2}x - 2$

D

$10\sin\, 2x$

Solution

(a) Applying ${C_1} \to {C_1} + {C_2}$,

we get $\left| {\,\begin{array}{*{20}{c}}1&{{{\cos }^2}x}&1\\1&{{{\sin }^2}x}&1\\2&{12}&2\end{array}\,} \right|\, = 0$.

Standard 12

Mathematics

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