Question

The value of \( \cos^2 67^\circ - \sin^2 23^\circ \) will be:

• A. \( \infty \)
• B. -1
• C. 0
• D. 1

Hint:

Use the identity \( \cos^2 \theta - \sin^2 \theta = \cos 2\theta \) to simplify such expressions.

Answer 1

The Correct Option is C

We can use the identity \( \cos^2 \theta - \sin^2 \theta = \cos(2\theta) \) to simplify the given expression. \[ \cos^2 67^\circ - \sin^2 23^\circ = \cos(2 \times 67^\circ) = \cos 134^\circ \] We know that \( \cos 134^\circ = -\cos 46^\circ \), and since \( \cos 46^\circ \) is a small positive value, we deduce that the value of \( \cos^2 67^\circ - \sin^2 23^\circ \) is effectively \( 0 \).
Step 1: Conclusion.
Thus, the value of the expression is 0.