# What is the Value of (sin2θ – cos2θ)

If tan θ = 3 sin θ then the value of (sin^{2}θ – cos^{2} θ) is

- 1
- 3
- 1/3
- None

**Answer: (4) None**

**Explanation:-**

tanθ = 3 sinθ

sinθ/cosθ = 3 sinθ

cosθ = 1/3

cos^{2θ} = 1/9

sinn2θ = 1 – cos^{2θ}

sin^{2θ} = 1 – 1/9

sin^{2θ} = (9 – 1)/9

sin^{2θ} = 8/9

Then, sin^{2θ} – cos^{2θ} = 8/9 – 1/9 = 7/9

Hence, the answer is (4) None