Question

The value of $\dfrac{\sin 27^\circ}{\cos 63^\circ}$ will be:

• A. 1
• B. -1
• C. 0
• D. $\dfrac{1}{2}$

Hint:

Use the co-function identity: $\sin(90^\circ - \theta) = \cos \theta$ to simplify such trigonometric ratios.

Answer 1

The Correct Option is A

Step 1: Using trigonometric identity.
We know that $\sin(90^\circ - \theta) = \cos \theta$. Hence, $\cos 63^\circ = \sin(27^\circ)$.

Step 2: Simplify the expression.
\[ \dfrac{\sin 27^\circ}{\cos 63^\circ} = \dfrac{\sin 27^\circ}{\sin 27^\circ} = 1 \]
Step 3: Conclusion.
Therefore, the value of $\dfrac{\sin 27^\circ}{\cos 63^\circ}$ is 1.