Explanation:

- Given that \(\tan \theta_1 = 1\), this means \(\theta_1 = 45^\circ\) or \(\pi/4\) radians. This is because \(\tan 45^\circ = 1\).

- We are also given that \(\sin \theta_2 = \frac{1}{\sqrt{2}}\), meaning \(\theta_2 = 45^\circ\) or \(\pi/4\) radians. This is because \(\sin 45^\circ = \frac{1}{\sqrt{2}}\).

- Using the angle addition formula for sine: \(\sin(\theta_1 + \theta_2) = \sin \theta_1 \cos \theta_2 + \cos \theta_1 \sin \theta_2\).

- Substituting the known values: \(\sin(45^\circ + 45^\circ) = \sin 90^\circ\).

- \(\sin 90^\circ = 1\).

Correct Option:

- Option 1: 1