Question

What is the value of \( \csc 31^\circ \sec 59^\circ \)?

• A. 0
• B. 1
• C. Undefined
• D. 2

Hint:

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

Answer 1

The Correct Option is A

We are asked to compute \( \csc 31^\circ \sec 59^\circ \). Recall that \( \csc \theta = \frac{1}{\sin \theta} \) and \( \sec \theta = \frac{1}{\cos \theta} \). Thus: \[ \csc 31^\circ \sec 59^\circ = \frac{1}{\sin 31^\circ} \times \frac{1}{\cos 59^\circ}. \] Using the identity \( \sin \theta = \cos (90^\circ - \theta) \), we can write: \[ \sin 31^\circ = \cos 59^\circ. \] Therefore: \[ \csc 31^\circ \sec 59^\circ = \frac{1}{\cos 59^\circ} \times \frac{1}{\cos 59^\circ} = 1. \] Thus, the value of \( \csc 31^\circ \sec 59^\circ \) is \( 1 \).