Question

Value of \( \frac{\sin 15^\circ}{\cos 75^\circ} \) will be:

• A. 1
• B. 0
• C. 2
• D. -1

Hint:

For complementary angles, \( \cos \theta = \sin (90^\circ - \theta) \). Use this identity to simplify trigonometric expressions.

Answer 1

The Correct Option is A

We are asked to find the value of \( \frac{\sin 15^\circ}{\cos 75^\circ} \).
Step 1: Use the identity for sine and cosine.
We know that: \[ \cos 75^\circ = \sin 15^\circ \] This is because \( 75^\circ \) and \( 15^\circ \) are complementary angles, meaning \( 75^\circ + 15^\circ = 90^\circ \), and for complementary angles, \( \cos \theta = \sin (90^\circ - \theta) \).
Step 2: Simplify the expression.
Now, we can substitute \( \cos 75^\circ \) with \( \sin 15^\circ \): \[ \frac{\sin 15^\circ}{\cos 75^\circ} = \frac{\sin 15^\circ}{\sin 15^\circ} = 1 \]
Step 3: Conclusion.
Therefore, the value of \( \frac{\sin 15^\circ}{\cos 75^\circ} \) is 1. The correct answer is (A).