Question

What is the value of \( \frac{\sin 42^\circ}{\cos 48^\circ} \)?

• A. 0.5
• B. 1
• C. \( \frac{\sqrt{2}-1}{\sqrt{2}} \)
• D. None of these

Hint:

Using trigonometric identities can simplify problems significantly. Here, \( \sin \theta = \cos (90^\circ - \theta) \) was used to simplify the expression.

Answer 1

The Correct Option is B

Using the trigonometric identity \( \sin \theta = \cos(90^\circ - \theta) \), we have: \[ \sin 42^\circ = \cos(90^\circ - 42^\circ) = \cos 48^\circ \] Thus, the expression simplifies to: \[ \frac{\sin 42^\circ}{\cos 48^\circ} = \frac{\cos 48^\circ}{\cos 48^\circ} = 1 \] Therefore, the correct answer is 1.