Няколко задачи от тригонометрия

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Някойй може ли да помогне за някоя от задачите

[Mark]

[tex]tg(\frac{\pi}{4}-\frac{\alpha}{2})=\frac{cos\alpha}{1+sin\alpha}[/tex]
[tex]\frac{cos\alpha}{1+sin\alpha}=[/tex][tex]\frac{cos^2\frac{\alpha}{2}-sin^2\frac{\alpha}{2}}{{sin^2\frac{\alpha}{2}+cos^2\frac{\alpha}{2}+2sin\frac{\alpha}{2}cos\frac{\alpha}{2}}[/tex][tex]=\frac{cotg\frac{\alpha}{2}-1}{cotg\frac{\alpha}{2}+1}[/tex][tex]=tg(\frac{\pi}{4}-\frac{\alpha}{2})[/tex]

[tex]tg4\alpha+\frac{1}{cos4\alpha}[/tex][tex]=\frac{cos2\alpha+sin2\alpha}{cos2\alpha-sin2\alpha}[/tex]
[tex]\frac{sin4\alpha}{cos4\alpha}+\frac{1}{cos4\alpha}[/tex][tex]=\frac{(cos2\alpha+sin2\alpha)^2}{(cos2\alpha-sin2\alpha).(cos2\alpha+sin2\alpha}[/tex][tex]=\frac{cos2\alpha+sin2\alpha}{cos2\alpha-sin2\alpha}[/tex]

[tex]1+sin\alpha=sin(\frac{\pi}{2})+sin\alpha[/tex][tex]=2sin^2(\frac{\pi}{4}+\frac{\alpha}{2})[/tex]

[tex]1+tg{\alpha}=tg{\frac{\pi}{4}+tg{\alpha}}=\frac{\sin({\frac{\pi}{4}+\alpha})}{\cos{\frac{\pi}{4}}\cos{\alpha}}=\frac{\sqrt{2}\sin({\frac{\pi}{4}+\alpha})}{cos{\alpha}}[/tex]

[tex]\frac{sin4\alpha}{(1+ cos4\alpha)}.\frac{cos2\alpha}{(1+cos2\alpha )}\frac{cos\alpha}{(1 + cos\alpha )}[/tex][tex]= \frac{sin4\alpha}{2cos^22\alpha }.\frac{cos2\alpha}{2cos^2 \alpha}.\frac{cos\alpha}{(1+cos\alpha )}[/tex][tex]=\frac{sin\alpha}{1+cos\alpha}[/tex]

[tex]cotg{\alpha}-tg{\beta }=\frac{cos { \alpha }}{sin{\alpha}}-\frac{\sin{\beta}}{cos{\beta}}=\frac{cos{\alpha}cos{\beta}-sin{\alpha}sin{\beta}}{sin{\alpha}cos{\beta}}=\frac{cos({\alpha+\beta})}{sin{\alpha}cos{\beta}}[/tex]

Ако някои му се занимава, нека ти реши останалите..

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Mерси ^^
Няма нужда другите да ми ги решавате, оправих се.