If θ is an acute angle and sin θ = cos θ, find the value of θ and hence, find the value of 2 tan² θ + sin² θ - 1.

Given,

sin θ = cos θ

⇒ tan θ = 1

⇒ tan θ = tan 45°

⇒ θ = 45°.

Substituting value in 2 tan² θ + sin² θ - 1 we get :

⇒ 2 tan² 45° + sin² 45° - 1

⇒ 2(1)² + $\Big(\dfrac{1}{\sqrt{2}}\Big)^2 -1$

⇒ 2 + $\dfrac{1}{2}$ - 1

⇒ $1\dfrac{1}{2}$.

Hence, 2 tan² θ + sin² θ - 1 = $1\dfrac{1}{2}$.