Question

Evaluate \( \sin 54^\circ - \cos 36^\circ \).

• A. \(0\)
• B. \(1\)
• C. \(2\)
• D. \(-1\)

Hint:

Remember co-function pairs: \(\sin(90^\circ-\theta)=\cos\theta\) and \(\cos(90^\circ-\theta)=\sin\theta\).

Answer 1

The Correct Option is A

Step 1: Use the co-function identity.
\(\sin(90^\circ-\theta)=\cos\theta\). With \(\theta=36^\circ\), we get \(\sin 54^\circ=\cos 36^\circ\).
Step 2: Substitute and simplify.
\[ \sin 54^\circ - \cos 36^\circ = \cos 36^\circ - \cos 36^\circ = 0. \]