Q235 / 270 · NDA 2010 (Phase 2) · Mathematics

What is the value of $\sin 15^{\circ} \sin 75^{\circ}$ ?

  • Correct answer
    A
    $1 / 4$
  • B
    $1 / 8$
  • C
    $1 / 16$
  • D
    1

Solution

$\begin{aligned} & \sin \left(45^{\circ}-30^{\circ}\right) \cdot \sin \left(45^{\circ}+30^{\circ}\right) \\ & =\sin ^2 45^{\circ}-\sin ^2 30^{\circ} \\ & =\left(\frac{1}{\sqrt{2}}\right)^2-\left(\frac{1}{2}\right)^2=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}\end{aligned}$

Hence, the correct answer is option: 'A'.

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