Q172 / 270 · NDA 2021 (Phase 1) · Mathematics

What is the value of the following? $\left(\sin 24^{\circ}+\cos 66^{\circ}\right)\left(\sin 24^{\circ}-\cos 66^{\circ}\right)$

  • A
    $-1$
  • Correct answer
    B
    $0$
  • C
    $1$
  • D
    $2$

Solution

$\begin{aligned} & \left(\sin 24^{\circ}+\cos 66^{\circ}\right)\left(\sin 24^{\circ}-\cos 66^{\circ}\right) \\ & =\sin ^2 24^{\circ}-\cos ^2 66^{\circ}\end{aligned}$ $\begin{aligned} & =\sin ^2 24^{\circ}-\cos ^2\left(90^{\circ}-24^{\circ}\right) \\ & =\sin ^2 24^{\circ}-\sin ^2 24^{\circ}=0\end{aligned}$

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

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