If tan θ = x − y , the value of sinθ is

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If tan θ = x − y , the value of sinθ is equal to [If 0° ≤ θ ≤ 90°]
x + y

1. x − y
  √2(x² + y²)
2. x + y
  √2(x² + y²)
3. x + y
  √2(x² − y²)
4. x − y
  √2(x² − y²)

Correct Option: A

Here,

tan θ =	x - y
	x + y

Consider ∆ABC,

Using pythagoras theorem, we get
AC² = AB² + BC²
⇒ AC² = (x + y)² + (x – y)²
= x² + y² + 2xy + x² + y² – 2xy
AC² = 2 (x² + y²)
AC = √2(x² + y²)
As θ lies in first quadrant,
∵ sinq will be +ve

sinθ =	BC
	AC

sinθ =	x - y
	√2(x² + y²)

If tan θ =	x − y	, the value of sinθ is equal to [If 0° ≤ θ ≤ 90°]
	x + y