If $\cos heta = \dfrac{\sqrt{3}}{2}$ and $\sin\phi = \dfrac{1}{2}$, then $ an( heta + \phi)$ is :

Question

If $\cos	heta = \dfrac{\sqrt{3}}{2}$ and $\sin\phi = \dfrac{1}{2}$, then $	an(	heta + \phi)$ is :

Accepted Answer

## Model Answer $\cos	heta = \dfrac{\sqrt{3}}{2} \Rightarrow 	heta = 30°$ and $\sin\phi = \dfrac{1}{2} \Rightarrow \phi = 30°$. So $	heta + \phi = 60°$, and $	an 60° = \sqrt{3}$. **Answer: (A) $\sqrt{3}$** ## Explanation From Table 8.1 (Ch. 8): $\cos 30° = \frac{\sqrt{3}}{2}$ and $\sin 30° = \frac{1}{2}$, so both angles are 30°. Their sum is 60°, and $	an 60° = \sqrt{3}$. Identify standard angles from the table — this is the key skill tested here.

Mathematics — Standard (041) — CBSE Class 10 board question