Помогите решить очень быстро. Created by nika1299. algebra-ru

Помогите решить очень быстро...

Evgenia4836

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NNNLLL54

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$tg\Big(\dfrac{\pi}{4}+\dfrac{a}{2}\Big)\cdot \dfrac{1-sina}{cosa}=\dfrac{tg\frac{\pi}{4}+tg\frac{a}{2}}{1-tg\frac{\pi}{4}\cdot tg\frac{a}{2}}\cdot \dfrac{cos^2\frac{a}{2}+sin^2\frac{a}{2}-2\, sin\frac{a}{2}\cdot cos\frac{a}{2}}{cos^2\frac{a}{2}-sin^2\frac{a}{2}}=$

$=\dfrac{1+\frac{sin\, a/2}{cos\, a/2}}{1-\frac{sin\, a/2}{cos\, a/2}}\cdot \dfrac{(cos\frac{a}{2}-sin\frac{a}{2})^2}{(cos\frac{a}{2}-sin\frac{a}{2})(cos\frac{a}{2}+sin\frac{a}{2})}=\dfrac{cos\frac{a}{2}+sin\frac{a}{2}}{cos\frac{a}{2}-sin\frac{a}{2}}\cdot \dfrac{cos\frac{a}{2}-sin\frac{a}{2}}{cos\frac{a}{2}+sin\frac{a}{2}}=1$

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