Докажете тъждеството

[ceneto18]

[tex]a)\frac{tg\alpha + tg\beta}{tg(\alpha + \beta)} + \frac{tg\alpha - tg\beta}{tg( \alpha - \beta)} = 2[/tex]

[tex]b)\frac{tg\alpha - tg\beta}{tg(\alpha - \beta)} - \frac{tg\alpha + tg\beta}{tg( \alpha + \beta)} = 2tg\alpha.tg\beta[/tex]

[tex]c) sin^{6} \alpha + cos^{6} \alpha = 1 - \frac{3}{4}sin^{2}2\alpha[/tex]

[tex]d) \frac{2 - sin4\alpha.cotg2\alpha}{sin4\alpha} = tg2\alpha[/tex]

[tex]e) cos^{3}\alpha.cos3\alpha + sin^{3}\alpha.sin3\alpha = cos^{3}2\alpha[/tex]

[tex]f)\frac{1 + sin2\alpha}{cos2\alpha} = tg(\frac{\pi }{4} + \alpha)[/tex]

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