Question

Please help me. Trigonometry(Half-Angle)​

Answer 1

$\frac{cosa}{1 + sina} \\ \\ = \frac{cos2 \frac{a}{2} }{1 + sin2 \frac{a}{2} } \\ \\ = \frac{ {cos}^{2} \frac{a}{2} - {sin}^{2} \frac{a}{2} }{ {sin}^{2} \frac{a}{2} + {cos}^{2} \frac{a}{2} + 2sin \frac{a}{2} cos \frac{a}{2} } \\ \\ = \frac{ {cos}^{2} \frac{a}{2} - {sin}^{2} \frac{a}{2} }{( {cos \frac{a}{2} + sin \frac{a}{2} })^{2} } \\ \\ = \frac{cos \frac{a}{2} - sin \frac{a}{2} }{cos \frac{a}{2} + sin \frac{a}{2} } \\ \\ = \frac{1 - tan \frac{a}{2} }{1 + tan \frac{a}{2} } (devided \: by \: cos \frac{a}{2}) \\ \\ = \frac{tan \frac{\pi}{4} - tan \frac{a}{2} }{1 + tan \frac{\pi}{4} tan \frac{a}{2} } \\ \\ = tan( \frac{\pi}{4} - \frac{a}{2} )$