Question

Without using tables, find:
$\frac{\sin {10}^o+\sin {50}^o-\sin {80}^o+\sin {140}^o}{\sqrt{2}.\sin {25}^o}$

Answer 1

$\frac{{\sin 10}^0+{\sin 50}^0+{\sin 140}^0-{\sin 80}^0}{\sqrt{2}{\sin 25}^0}$

$\because sinC+sinD=2\sin \left(\frac{C+D}{2}\right)\cos \left(\frac{C-D}{2}\right)$

$sinC-sinD=2\cos \left(\frac{C+D}{2}\right)\sin \left(\frac{C-D}{2}\right)$

$\Rightarrow \frac{2(\sin \left({30}^0\right){\cos 20}^0+2\cos \left({110}^0\right)\sin \left({30}^0\right))}{\sqrt{2}\sin {25}^0}$

$\Rightarrow \frac{2{\sin 30}^0({\cos 20}^0+{\cos 110}^0)}{\sqrt{2}\sin {25}^0}$

${\sin 30}^0=1/2$

$cosC+cosD=2\cos \left(\frac{C+D}{2}\right)\cos \left(\frac{C-D}{2}\right)$

wrong question.

10th solution