If sin x = cos x and x is acute, state the value of x.

sin x = cos x

As we know that sin² x + cos² x = 1

⇒ sin² x + sin² x = 1

⇒ 2sin² x = 1

⇒ sin² x = $\dfrac{1}{2}$

⇒ sin x = $\dfrac{1}{\sqrt2}$

⇒ sin x = sin 45°

⇒ x = 45°

Hence, the value of x = 45°.