Question

If 4 cos²θ - 3 sin²θ + 2 = 0, then the value of tanθ is (where 0 ≤ θ < 90°)

• A. $$\sqrt{2}$$
• B. $$\sqrt{6}$$
• C. $$\frac{1}{\sqrt{3}}$$
• D. 1

Answer 1

Answer:

$$\sqrt{6}$$

Solution:

Given

4 cos² θ - 3 sin² θ + 2 = 0

Formula:

sin²θ + cos²θ = 1

tan²θ = sin²θ/cos²θ

Calculation:

4 cos²θ - 3 sin²θ + 2 = 0

⇒ 4 cos²θ - 3 (1 - cos²θ) + 2 = 0

⇒ 4 cos²θ - 3 + 3 cos²θ + 2 = 0

⇒ 7 cos²θ - 1 = 0

⇒ 7 cos²θ = 1

⇒ cos²θ = 1/7

sin²θ + cos²θ = 1

⇒ sin²θ = 1 - 1/7

⇒ sin²θ = 6/7

Now,

tan²θ = sin²θ/cos²θ

⇒ tan²θ = (6/7)/(1/7)

⇒ tan²θ = 6

∴ tanθ = √6