If tan 3x = sin 45° cos 45° + sin 30°, find the value of x.

Given,

$\Rightarrow \text{tan 3x = sin 45° cos 45° + sin 30°} \\[1em] \Rightarrow \text{tan 3x} = \dfrac{1}{\sqrt{2}} \times \dfrac{1}{\sqrt{2}} + \dfrac{1}{2} \\[1em] \Rightarrow \text{tan 3x} = \dfrac{1}{2} + \dfrac{1}{2} \\[1em] \Rightarrow \text{tan 3x} = 1 \\[1em] \Rightarrow \text{tan 3x = tan 45°} \\[1em] \Rightarrow 3x = 45° \\[1em] \Rightarrow x = \dfrac{45\degree}{3} \\[1em] \Rightarrow x = 15°.$

Hence, x = 15°.