Q64 / 150 · MHT CET 2020 (15 Oct Shift 1) · Mathematics

$\sin 690^{\circ} \times \sec 240^{\circ}=$

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

Solution

$\sin 690^{\circ} \times \sec 240^{\circ}$ $=\sin \left(1 \times 360^{\circ}+330^{\circ}\right) \times \sec \left(180^{\circ}+60^{\circ}\right)$ $=\sin 330^{\circ} \times\left(-\sec 60^{\circ}\right)$ $=\sin \left(2 \pi-30^{\circ}\right) \times(-2)$ $=-2\left(-\sin 30^{\circ}\right)=(-2)\left(-\frac{1}{2}\right)=1$

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

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