If θ is an acute angle and sin θ = cos θ, then find the value of 2tan²θ + sin²θ – 1.

We have, sin θ = cos θ

Dividing both sides by cos θ,

⇒ tanθ = 1

⇒ tanθ = tan45°

⇒  θ= 45°

∴ 2tan²θ + sin²θ – 1

=  2tan²45°+ sin²45° – 1

$=2(1{)}^2+{\left(\frac{1}{\sqrt{2}}\right)}^2-1$

$=\frac{3}{2}$

Hence, the value of 2tan²θ + sin²θ – 1 is $\frac{3}{2}.$