Question
Download Solution PDFWhat is sin12° sin48° equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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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