Equation x + (t + x) + (t - x) = 2 has real solution, then t can be

Given, $\sin x + \cos \left(t + x\right) + \cos \left(t - x\right) = 2$

$⇒ \sin x + 2\cos t \cdot \cos x = 2$

For real solution

$\sqrt{1 + 4\cos^{2}t} \ge 2$

$⇒ \cos^{2}t \ge \dfrac{3}{4}$

$⇒ - \dfrac{1}{2} \le \sin t \le \dfrac{1}{2}$

Hence, option (a) is correct.