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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
Evaluate: $\left|\begin{array}{ll}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ}\end{array}\right|$
  • ✓
    $0$
  • B
    $1$
  • C
    $2$
  • D
    $3$
✓

Answer

Correct option: A.
$0$
We have, $\left|\cos 15^{\circ} \sin 15^{\circ} \sin 75^{\circ} \cos 75^{\circ}\right|$
$=\cos 15^{\circ} \times \cos 75^{\circ}-\sin 15^{\circ} \times \sin 75^{\circ}=\cos \left(15^{\circ}+75^{\circ}\right)$
$=\cos 90^{\circ}$
$=0$

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