Question

If \( \tan(\pi \cos x) = \cot(\pi \sin x) \), then what is \( \sin \left( \frac{\pi}{2} + x \right) \)?

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

Hint:

Use trigonometric identities such as \( \tan(A + B) \) and \( \sin \left( \frac{\pi}{2} + x \right) \) to simplify complex equations.