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Question
The value of `cos^2 48^@ - sin^2 12^@` is ______.
Options
- `(sqrt5 + 1)/(2 sqrt2)`
- `(sqrt5 + 1)/(5)`
- `(sqrt5 - 1)/(8)`
- `(sqrt5 + 1)/(8)`
Solution
The value of `cos^2 48^@ - sin^2 12^@` is `bbunderline((sqrt5 + 1)/(8))`.
Explanation:
\[\cos^2 48° - \sin^2 12°\]
\[ = \cos\left( 48° + 12° \right)\cos\left( 48° - 12° \right) \left[ \cos\left( A + B \right)\cos\left( A - B \right) = \cos^2 A - \sin^2 B \right]\]
\[ = \cos60° \cos36° \]
\[ = \frac{1}{2} \times \left( \frac{\sqrt{5} + 1}{4} \right)\]
\[ = \frac{\sqrt{5} + 1}{8}\]
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