Question

if tantheta = 2xy/ x²-y² prove that sintheta= 2 xy/ x²+y²​

Answer 1

As −1≤sinθ≤1

⇒0≤sin

2

θ≤1

⇒0≤

2xy

x

2

+y

2

≤1

Now using

2xy

x

2

+y

2

≥0⇒x

2

+y

2

≥0 ...(1)

And

2xy

x

2

+y

2

≤1⇒x

2

+y

2

≤2xy

⇒(x−y)

2

≤0⇒x=y ...(2)

and x,y



=0