Let theta inleft(0, frac{pi}{2}right). If the | vedclass

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Question

$Case-I$

$\left| {{\mkern 1mu} \begin{array}{*{20}{c}} {1 + {{\cos }^2}	heta }&{{{\sin }^2}	heta }&{4\sin 3	heta }\ {{{\cos }^2}	heta

Vedclass · Accepted Answer

$\frac{7 \pi}{18}$

Vedclass · Answer

$Case-I$

$\left| {{\mkern 1mu} \begin{array}{*{20}{c}} {1 + {{\cos }^2}	heta }&{{{\sin }^2}	heta }&{4\sin 3	heta }\ {{{\cos }^2}	heta }&{1 + {{\sin }^2}	heta }&{4\sin 3	heta }\ {{{\cos }^2}	heta }&{{{\sin }^2}	heta }&{1 + 4\sin 3	heta } \end{array}{\mkern 1mu} } ight| = 0$

$\mathrm{C}_{1} ightarrow \mathrm{C}_{1}+\mathrm{C}_{2}$

$\left| {{\mkern 1mu} \begin{array}{*{20}{c}} 2&{{{\sin }^2}	heta }&{4\sin 3	heta }\ 2&{1 + {{\sin }^2}	heta }&{4\sin 3	heta }\ 1&{{{\sin }^2}	heta }&{1 + 4\sin 3	heta } \end{array}{\mkern 1mu} } ight| = 0$

$\mathrm{R}_{1} ightarrow \mathrm{R}_{1}-\mathrm{R}_{2}, \mathrm{R}_{2} ightarrow \mathrm{R}_{2}-\mathrm{R}_{3}$

$\left| {{\mkern 1mu} \begin{array}{*{20}{c}} 0&{ - 1}&0\ 1&1&{ - 1}\ 1&{{{\sin }^2}	heta }&{1 + 4\sin 3	heta } \end{array}{\mkern 1mu} } ight| = 0$

or $4 \sin 3 	heta=-2$

$\sin 3 	heta=-\frac{1}{2}$

$	heta=\frac{7 \pi}{18}$

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