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Provide solution for RD Sharma maths class 12 chapter Determinants exercise 5.1 question 2 subquestion (iii)

Answers (1)

Answer:

0

Hint:

Determinant matrix must be square (i.e. same number of rows and columns)

Given:

\begin{aligned} \left|\begin{array}{cc} \cos 15^{\circ} & \sin 15^{\circ} \\ -\sin 75^{\circ} & \cos 75^{\circ} \end{array}\right|\\ \end{aligned}

Solution:

\begin{aligned} &\begin{aligned} \mathrm{D} &=\mathrm{a}_{11} \times \mathrm{C}_{11}+\mathrm{a}_{21} \times \mathrm{C}_{21} \\ &=\cos 15^{\circ}\left(\cos 75^{\circ}\right)+\left(\sin 15^{\circ}\left(-\sin 75^{\circ}\right)\right) \\ &=\cos 15^{\circ} \cos 75^{\circ}-\sin \left(90^{\circ}-15^{\circ}\right) \sin \left(90^{\circ}-75^{\circ}\right) \quad\left[\sin \left(90^{\circ}-\theta\right)=\cos \theta\right] \\ &=\cos 15^{\circ} \cos 75^{\circ}-\cos 75^{\circ} \cos 15^{\circ} \\ &=0 \end{aligned} \end{aligned}

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Gurleen Kaur

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