What is sin12° sin48° equal to? 

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. \(\frac{\sqrt5-1}{4}\)
  2. \(\frac{\sqrt5+1}{4}\)
  3. \(\frac{\sqrt5-1}{8}\)
  4. \(\frac{\sqrt5+1}{8}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{\sqrt5-1}{8}\)
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Concept:

Product-to-Sum Formulas:

  • The product-to-sum formulas are used to express products of sines and cosines as sums.
  • For sines, the formula is:

    \(\sin A \sin B = \frac{1}{2} [ \cos (A-B) - \cos (A+B) ] \)

 

Calculation:

⇒ sin12°.sin48° = \(\frac{2(sin12°.sin48°)}{2}\)

\(\frac{1}{2} [Cos 36° -Cos60°]\)

\(\frac{1}{2}[\frac{\sqrt5 +1}{4} -\frac{1}{2}] =\frac{\sqrt5 -1}{8}\)

 Option (c) is correct

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