Question

$\alpha$ + $\beta$ - $\gamma$ = $\pi$ Then $si{n}^2\beta$ - $si{n}^2\gamma$ =

• A. () ()
• B. sin sin
• C. Both A & B
• D. cos cos

Answer 1

The correct option is C

Both A & B

$si{n}^2\beta$ - $si{n}^2\gamma$

= $(sin\beta +sin\gamma )$ $(sin\beta -sin\gamma )$

Option A is correct

= 2 sin $\frac{(\beta +\gamma )}{2}$ . cos $\frac{(\beta -\gamma )}{2}$ . 2 cos $\frac{(\beta +\gamma )}{2}$ . sin $\frac{(\beta -\gamma )}{2}$

= 2 sin $\frac{(\beta +\gamma )}{2}$ . cos $\frac{(\beta +\gamma )}{2}$ $\times$ 2 sin $\frac{(\beta -\gamma )}{2}$ . cos $\frac{(\beta -\gamma )}{2}$

= sin $\{2\times \frac{(\beta +\gamma )}{2}\}\times sin\{2\times \frac{(\beta -\gamma )}{2}\}$

= sin $(\beta +\gamma )$ sin $(\beta -\gamma )$

So,option B is also correct