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CBSE Class 12 RD Sharma Maths Determinants Exercise 6.2
Exercise 6.2

Without expanding, show that the value of each of the following determinants is zero:$\left| \begin{matrix} {{\sin }^{2}}A & \cot A & 1 \\ {{\sin }^{2}}B & \cot B & 1 \\ {{\sin }^{2}}C & \cot C & 1 \\ \end{matrix} \right|$ where A,B,C are the angles of $\vartriangle ABC$

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$\left| \begin{matrix} {{\sin }^{2}}A & \cot A & 1  \\ {{\sin }^{2}}B & \cot B & 1  \\ {{\sin }^{2}}C & \cot C & 1  \\ \end{matrix} \right|$ Let $\vartriangle =\left|...

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Without expanding, show that the value of each of the following determinants is zero:$\left| \begin{matrix} {{\sin }^{2}}{{23}^{\circ }} & {{\sin }^{2}}{{67}^{\circ }} & \cos {{180}^{\circ }} \\ -{{\sin }^{2}}{{67}^{\circ }} & -{{\sin }^{2}}{{23}^{\circ }} & {{\cos }^{2}}{{180}^{\circ }} \\ \cos {{180}^{\circ }} & {{\sin }^{2}}{{23}^{\circ }} & {{\sin }^{2}}{{67}^{\circ }} \\ \end{matrix} \right|$

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$\left| \begin{matrix} {{\sin }^{2}}{{23}^{\circ }} & {{\sin }^{2}}{{67}^{\circ }} & \cos {{180}^{\circ }}  \\ -{{\sin }^{2}}{{67}^{\circ }} & -{{\sin }^{2}}{{23}^{\circ }} & {{\cos...

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Without expanding, show that the value of each of the following determinants is zero:$\left| \begin{matrix} \sin \alpha & \cos \alpha & \cos \left( \alpha +\delta \right) \\ \sin \beta & \cos \beta & \cos \left( \beta +\delta \right) \\ \sin \gamma & \cos \gamma & \cos \left( \gamma +\delta \right) \\ \end{matrix} \right|$

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$\left| \begin{matrix} \sin \alpha  & \cos \alpha  & \cos \left( \alpha +\delta  \right)  \\ \sin \beta  & \cos \beta  & \cos \left( \beta +\delta  \right)  \\ \sin \gamma  &...

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Without expanding, show that the value of each of the following determinants is zero:$\left| \begin{matrix} {{\left( {{2}^{x}}+{{2}^{-x}} \right)}^{2}} & {{\left( {{2}^{x}}-{{2}^{-x}} \right)}^{2}} & 1 \\ {{\left( {{3}^{x}}+{{3}^{-x}} \right)}^{2}} & {{\left( {{3}^{x}}-{{3}^{-x}} \right)}^{2}} & 1 \\ {{\left( {{4}^{x}}+{{4}^{-x}} \right)}^{2}} & {{\left( {{4}^{x}}-{{4}^{-x}} \right)}^{2}} & 1 \\ \end{matrix} \right|$

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$\left| \begin{matrix} {{\left( {{2}^{x}}+{{2}^{-x}} \right)}^{2}} & {{\left( {{2}^{x}}-{{2}^{-x}} \right)}^{2}} & 1  \\ {{\left( {{3}^{x}}+{{3}^{-x}} \right)}^{2}} & {{\left(...

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Without expanding, show that the value of each of the following determinants is zero:$\left| \begin{matrix} {{1}^{2}} & {{2}^{2}} & {{3}^{2}} & {{4}^{2}} \\ {{2}^{2}} & {{3}^{2}} & {{4}^{2}} & {{5}^{2}} \\ {{3}^{2}} & {{4}^{2}} & {{5}^{2}} & {{6}^{2}} \\ {{4}^{2}} & {{5}^{2}} & {{6}^{2}} & {{7}^{2}} \\ \end{matrix} \right|$

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$\left| \begin{matrix} {{1}^{2}} & {{2}^{2}} & {{3}^{2}} & {{4}^{2}}  \\ {{2}^{2}} & {{3}^{2}} & {{4}^{2}} & {{5}^{2}}  \\ {{3}^{2}} & {{4}^{2}} & {{5}^{2}} &...

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