Question

If θ is an acute angle and sinθ = cosθ, then the value of 2 tan²θ + sin²θ - 1 is equal to:
1. 1
2. -7
3. 3
4. \(\rm \frac{3}{2}\)

Answer 1

Correct Answer - Option 4 : \(\rm \frac{3}{2}\)

Given:

sinθ = cosθ   [Where θ is an acute angle ] 

Identity used:

sinx = cos(90° - x)

Calculation:

sinθ = sin(90° - θ)

⇒ θ = 90°- θ

⇒ 2θ = 90°

⇒ θ = 90°/2 = 45° 

Now, 2 tan2θ + sin2θ - 1 

⇒ 2 × 1 + (1/√2)² - 1

⇒ 2 + 1/2 - 1

⇒ 1 + 1/2 

⇒ 3/2 

∴ The required value = 3/2