математика

[Гост]

Ако някой може да ми помогне?

[math10.com]

[tex]\frac{1+sin {2\alpha}}{cos {2\alpha}}=\frac{sin^2\alpha +cos^2\alpha +2sin \alpha .cos\alpha }{cos^2 \alpha -sin^2 \alpha}=\frac{\cancel{(sin \alpha+cos \alpha )}(sin \alpha+cos \alpha )}{\cancel{(sin \alpha+cos \alpha )}(cos \alpha -sin \alpha)}=\frac{sin \alpha +sin{(90^\circ-\alpha)}}{sin{(90^\circ-\alpha)}-sin \alpha} =[/tex]

[tex]=\frac{2sin{(\frac{\alpha+90^\circ-\alpha}{2})}.cos{(\frac{\alpha-90^\circ+\alpha}{2})}}{2sin{(\frac{\alpha-90^\circ+\alpha}{2})}.cos{(\frac{\alpha+90^\circ-\alpha}{2})} }=\frac{\cancel{sin45^\circ}.cos{(\alpha -45^\circ)}}{ \cancel{cos45^\circ}.sin{(\alpha -45^\circ)}}=cotg {(\alpha -45^\circ)} =tg{(45 ^\circ +\alpha )}[/tex]