Question

\( \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ \) is:

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

Hint:

The identity: \[ \cos(A + B) = \cos A \cos B - \sin A \sin B \] is useful for sum and difference trigonometry problems.

Answer 1

The Correct Option is A

Using the trigonometric identity:
\[ \cos(A + B) = \cos A \cos B - \sin A \sin B \] Substituting \( A = 38^\circ \), \( B = 52^\circ \):
\[ \cos(38^\circ + 52^\circ) = \cos 90^\circ = 1 \]