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Mark the tick against the correct answer in the following: \left|\begin{array}{ll} \cos 15^{\circ} & \sin 15^{\circ} \\ \sin 15^{\circ} & \cos 15^{\circ} \end{array}\right|=?
A. 1
B. \frac{1}{2}
C. \frac{\sqrt{3}}{2}
D. none of these
CBSE | Class 12 | Determinants | Maths | RS Aggarwal
Mark the tick against the correct answer in the following: \left|\begin{array}{ll} \cos 15^{\circ} & \sin 15^{\circ} \\ \sin 15^{\circ} & \cos 15^{\circ} \end{array}\right|=?
A. 1
B. \frac{1}{2}
C. \frac{\sqrt{3}}{2}
D. none of these

Solution:

Option(C)
To find: Value of \left|\begin{array}{ll}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 15^{\circ} & \cos 15^{\circ}\end{array}\right|
Formula used: (i) \cos (A+B)=\cos A \cos B-\sin A \sin B
We have, \left|\begin{array}{ll}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 15^{\circ} & \cos 15^{\circ}\end{array}\right|
On expanding the above,
\Rightarrow\left\{\cos 15^{\circ}\right\}\left\{\cos 15^{\circ}\right\}-\left\{\sin 15^{\circ}\right\}\left\{\sin 15^{\circ}\right\}
On applying formula \cos (A+B)=\cos A \cos B-\sin A \sin B
\begin{array}{l} =\cos (15+15) \\ =\cos \left(30^{\circ}\right) \\ =\frac{\sqrt{3}}{2} \end{array}

i

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