Question

The value of \(\cos 54^\circ \cos 36^\circ - \sin 54^\circ \sin 36^\circ\) is:

• A. 0
• B. 1
• C. \(\frac{\sqrt{3}}{2}\)
• D. \(\frac{1}{\sqrt{2}}\)

Hint:

Remember the cosine addition formula: \(\cos(A + B) = \cos A \cos B - \sin A \sin B\). This is useful for simplifying expressions with multiple angles.

Answer 1

The Correct Option is A

We can use the trigonometric identity for the cosine of the sum of two angles: \[ \cos(A + B) = \cos A \cos B - \sin A \sin B \] Using this identity with \(A = 54^\circ\) and \(B = 36^\circ\), we get: \[ \cos 54^\circ \cos 36^\circ - \sin 54^\circ \sin 36^\circ = \cos(54^\circ + 36^\circ) = \cos 90^\circ = 0 \] Thus, the correct answer is option (1).