Find value of x, if :

cos x = cos 60° cos 30° - sin 60° sin 30°

Solving,

$\Rightarrow \text{cos x} = \dfrac{1}{2} \times \dfrac{\sqrt{3}}{2} - \dfrac{\sqrt{3}}{2} \times \dfrac{1}{2} \\[1em] \Rightarrow \text{cos x} = \dfrac{\sqrt{3}}{4} - \dfrac{\sqrt{3}}{4} \\[1em] \Rightarrow \text{cos x} = 0 \\[1em] \Rightarrow \text{cos x} = \text{cos 90°} \\[1em] \Rightarrow x = 90°.$

Hence, x = 90°.