Question

If $sin\alpha -sin\beta =m$ and $cos\alpha cos\beta =n$ then $cos(\alpha -\beta )=$

• A. $\frac{2+m^2+n^2}{2}$
• B. $\frac{m^2+n^2}{2}$
• C. $\frac{2-m^2-n^2}{2}$
• D. $\frac{m^2+n^2-mn}{2}$

Answer 1

The correct option is C $\frac{2-m^2-n^2}{2}$

Squaring and adding given equations, $2-2sin\alpha sin\beta -2cos\alpha cos\beta =m^2+n^2$
$\Rightarrow cos\alpha cos\beta +sin\alpha sin\beta =cos(\alpha -\beta )=\frac{2-m^2-n^2}{2}$