Q59 / 160 · AP EAMCET 2023 (15 May Shift 1) · Mathematics

$$ \sin 21^{\circ} \cos 9^{\circ}-\cos 84^{\circ} \cos 6^{\circ}= $$

  • A
    1
  • Correct answer
    B
    $\frac{1}{4}$
  • C
    $\frac{1}{2}$
  • D
    $\frac{3}{2}$

Solution

$\begin{aligned} & \text { } \sin 21^{\circ} \cos 9^{\circ}-\cos 84^{\circ} \cos 6^{\circ} \\ & =\frac{1}{2}\left[2 \sin 21^{\circ} \cos 9^{\circ}-2 \cos \left(90^{\circ}-6^{\circ}\right) \cdot \cos 6^{\circ}\right]\end{aligned}$ $\begin{aligned} & =\frac{1}{2}\left[\sin 30^{\circ}+\sin 12^{\circ}-2 \sin 6^{\circ} \cos 6^{\circ}\right] \\ & =\frac{1}{2}\left[\frac{1}{2}+\sin 12^{\circ}-\sin 12^{\circ}\right]=\frac{1}{4}\end{aligned}$

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

Relevant Questions