If $\sin 30^\circ \cdot an 45^\circ = \dfrac{\sqrt{k}}{2}$, then the value of $k$ is :

Question

If $\sin 30^\circ \cdot 	an 45^\circ = \dfrac{\sqrt{k}}{2}$, then the value of $k$ is :

Accepted Answer

## Model Answer $\sin 30° \cdot 	an 45° = \dfrac{1}{2} 	imes 1 = \dfrac{1}{2} = \dfrac{\sqrt{1}}{2}$ So, $k = \mathbf{1}$. **Option D** ## Explanation Use standard values: sin 30° = 1/2 and tan 45° = 1. Their product is 1/2. Matching with √k/2 gives √k = 1, so k = 1. Examiners expect you to recall Table 8.1 values directly and substitute — no working beyond two steps is needed for 1 mark.

Mathematics — CBSE Class 10 board question