Question

The value of \( \dfrac{\sin 15^\circ}{\cos 75^\circ} \) will be:

• A. 1
• B. 0
• C. 2
• D. -1

Hint:

Use co-function identities like \( \sin \theta = \cos (90^\circ - \theta) \) to simplify expressions easily.

Answer 1

The Correct Option is A

Step 1: Use the trigonometric co-function identity.
\[ \cos (90^\circ - \theta) = \sin \theta \]
Step 2: Simplify.
\[ \cos 75^\circ = \cos (90^\circ - 15^\circ) = \sin 15^\circ \]
Step 3: Substitute.
\[ \dfrac{\sin 15^\circ}{\cos 75^\circ} = \dfrac{\sin 15^\circ}{\sin 15^\circ} = 1 \]
Step 4: Final answer.
\[ \boxed{1} \]