Question

\[ \frac{\text{cosec} 42^\circ}{\sec 48^\circ} \times \frac{\cos 37^\circ}{\sin 53^\circ} = \]

• A. 0
• B. \( \frac{1}{2} \)
• C. 1
• D. 2

Hint:

Using identities like \( \sin(90^\circ - \theta) = \cos \theta \) simplifies expressions involving complementary angles effectively.

Answer 1

The Correct Option is C

Step 1: Utilize known trigonometric identities for simplification: \[ \frac{\text{cosec} 42^\circ}{\sec 48^\circ} \times \frac{\cos 37^\circ}{\sin 53^\circ} = \frac{1/\sin 42^\circ}{1/\cos 48^\circ} \times \frac{\cos 37^\circ}{\cos 37^\circ} \] Step 2: Applying \( \sin 53^\circ = \cos 37^\circ \): \[ \frac{\cos 48^\circ}{\sin 42^\circ} = 1 \] Thus, the correct answer is \( \boxed{1} \).