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NDA 2 2024 Maths, question 29

Topic: Trigonometry

Q29

What is sin⁡12∘sin⁡48∘\sin 12^{\circ}\sin 48^{\circ} equal to?

  1. (a) 5−14\frac{\sqrt{5}-1}{4}
  2. (b) 5+14\frac{\sqrt{5}+1}{4}
  3. (c) 5−18\frac{\sqrt{5}-1}{8}Correct answer
  4. (d) 5+18\frac{\sqrt{5}+1}{8}

Solution.

Answer: (c) 5−18\frac{\sqrt{5}-1}{8}

  1. Product-to-sum gives 2sin12°sin48°=cos36°−cos60°.
  2. Since cos36°=(1+√5)/4 and cos60°=1/2, the product is (√5−1)/8.