# Find the the value given determinant $\left| {\begin{array}{*{20}{c}}

{\cos {{15}^ \circ }}&{\sin {{15}^ \circ }} \\

{\sin {{75}^ \circ }}&{\cos {{75}^ \circ }}

\end{array}} \right|$

A.$1$

B. $0$

C. $2$

D. $3$

Answer

Verified

367.8k+ views

Hint: This question can be solved by simply solving the determinant.

Given determinant is

$\left| {\begin{array}{*{20}{c}}

{\cos {{15}^ \circ }}&{\sin {{15}^ \circ }} \\

{\sin {{75}^ \circ }}&{\cos {{75}^ \circ }}

\end{array}} \right|$

Now on solving the determinant we get,

$\cos {75^ \circ } \cdot \cos {15^ \circ } - \sin {75^ \circ } \cdot \sin {15^ \circ }$

Now we know that,

$\cos \left( {A + B} \right) = \cos A \cdot \cos B - \sin A \cdot \sin B$

Using the above equation we get,

$

\cos \left( {{{75}^ \circ } + {{15}^ \circ }} \right) \\

{\text{or }}\cos \left( {{{90}^ \circ }} \right) \\

= 0 \\

$

Therefore, the correct option is (B).

Note: These types of questions can be solved by simply solving the determinant. Here in this question we simply solve the determinant and then we apply the formula of $\cos \left( {A + B} \right)$ and then we get our answer.

Given determinant is

$\left| {\begin{array}{*{20}{c}}

{\cos {{15}^ \circ }}&{\sin {{15}^ \circ }} \\

{\sin {{75}^ \circ }}&{\cos {{75}^ \circ }}

\end{array}} \right|$

Now on solving the determinant we get,

$\cos {75^ \circ } \cdot \cos {15^ \circ } - \sin {75^ \circ } \cdot \sin {15^ \circ }$

Now we know that,

$\cos \left( {A + B} \right) = \cos A \cdot \cos B - \sin A \cdot \sin B$

Using the above equation we get,

$

\cos \left( {{{75}^ \circ } + {{15}^ \circ }} \right) \\

{\text{or }}\cos \left( {{{90}^ \circ }} \right) \\

= 0 \\

$

Therefore, the correct option is (B).

Note: These types of questions can be solved by simply solving the determinant. Here in this question we simply solve the determinant and then we apply the formula of $\cos \left( {A + B} \right)$ and then we get our answer.

Last updated date: 30th Sep 2023

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