Question

The value of $\frac{\sin 31^\circ}{\cos 59^\circ}$ will be:

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Hint:

Remember that $\sin \theta = \cos (90^\circ - \theta)$. This is useful for simplifying trigonometric expressions.

Answer 1

The Correct Option is C

Step 1: Use the trigonometric identity.
We know that: \[ \sin \theta = \cos(90^\circ - \theta) \] Thus: \[ \sin 31^\circ = \cos(90^\circ - 31^\circ) = \cos 59^\circ \]
Step 2: Substitute this into the given expression.
So, \[ \frac{\sin 31^\circ}{\cos 59^\circ} = \frac{\cos 59^\circ}{\cos 59^\circ} = 1 \]
Step 3: Conclusion.
Therefore, the value of $\frac{\sin 31^\circ}{\cos 59^\circ}$ is $1$.