If sin α + sin β = a and cos α – cos β = b, then tan(α - β)/2

1.	If sin α + sin β = a and cos α – cos β = b, then tan(α - β)/2 = A. - (a/b)B. - (b/a)C. √(a2+b2)D. None of these
Answer» Option : (B) sin α + sin β = a ⇒ 2 sin\(\frac{\alpha+\beta}{2}\)cos\(\frac{\alpha-\beta}{2}\) = a …(I) cos α – cos β = b ⇒ - 2sin\(\frac{\alpha+\beta}{2}\)sin\(\frac{\alpha-\beta}{2}\) = b …(II) Dividing equation (II) by equation (I) – - tan\(\frac{\alpha-\beta}{2}\) = \(\frac{b}{a}\) Or, tan\(\frac{\alpha-\beta}{2}\) = \(-\frac{b}{a}\)

If sin α + sin β = a and cos α – cos β = b, then tan(α - β)/2 = A. - (a/b)B. - (b/a)C. √(a2+b2)D. None of these

Answer»

Option : (B)

sin α + sin β = a

⇒ 2 sin\(\frac{\alpha+\beta}{2}\)cos\(\frac{\alpha-\beta}{2}\) = a …(I)

cos α – cos β = b

⇒ - 2sin\(\frac{\alpha+\beta}{2}\)sin\(\frac{\alpha-\beta}{2}\) = b …(II)

Dividing equation (II) by equation (I) –

- tan\(\frac{\alpha-\beta}{2}\) = \(\frac{b}{a}\)

Or,

tan\(\frac{\alpha-\beta}{2}\) = \(-\frac{b}{a}\)