Multiple choice

Find the value of $\displaystyle \sin 18^{\circ}\mathrm{cosec} 54^{\circ}\mathrm{cosec} 36^{\circ}\sec 72^{\circ}\cos 54^{\circ}\cos 36^{\circ}.$

  1. $1$
  2. $0$
  3. $2$
  4. $-1$
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A Correct answer
Explanation

sin 18 = (sqrt(5)-1)/4. cos 54 = sin 36. cos 36 = sin 54. The expression simplifies: sin 18 * (1/sin 54) * (1/sin 36) * (1/cos 72) * cos 54 * cos 36. Since cos 72 = sin 18, the terms cancel out to 1.

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