Помогите пожалуйста 117 ( 2,4)

117.2 [latex] \frac{ 1 + tg{ \alpha } tg{ \beta } }{ 1 - tg{ \alpha } tg{ \beta } } = \frac{ ( 1 + tg{ \alpha } tg{ \beta } ) cos{ \alpha } cos{ \beta } }{ ( 1 - tg{ \alpha } tg{ \beta } ) cos{ \alpha } cos{ \beta } } = \frac{ cos{ \alpha } cos{ \beta } + sin{ \alpha } sin{ \beta } }{ cos{ \alpha } cos{ \beta } - sin{ \alpha } sin{ \beta } } = \frac{ cos{ ( \alpha - \beta ) } }{ cos{ ( \alpha + \beta ) } } \ ; [/latex] 117.4 [latex] cos{ \frac{ \alpha }{2} }ctg{ \frac{ \alpha }{4} } + sin{ \frac{ \alpha }{2} } = cos{ \frac{ \alpha }{2} }ctg{ \frac{ \alpha }{4} } + sin{ \frac{ \alpha }{2} }tg{ \frac{ \alpha }{4} }ctg{ \frac{ \alpha }{4} } = \\\\ = ctg{ \frac{ \alpha }{4} } ( cos{ \frac{ \alpha }{2} } + sin{ \frac{ \alpha }{2} }tg{ \frac{ \alpha }{4} } ) = ctg{ \frac{ \alpha }{4} } ( cos{ \frac{ \alpha }{2} } + sin{ \frac{ \alpha }{2} } \cdot \frac{ 1 - cos{ \frac{ \alpha }{2} } }{ sin{ \frac{ \alpha }{2} } } ) = \\\\ = ctg{ \frac{ \alpha }{4} } ( cos{ \frac{ \alpha }{2} } + [ 1 - cos{ \frac{ \alpha }{2} } ] ) = ctg{ \frac{ \alpha }{4} } \ ; [/latex]

117.2 (1+tqαtqβ)/(1-tqαtqβ) =(1+sinαsinβ/cosαcosβ)/(1-sinαsinβ/cosαcosβ) = (cosαcosβ +sinαsinβ)/(cosαcosβ -sinαsinβ) =cos(α-β)/cos(α+β). ------- 117.4 cosα/2*ctqα/4+ sinα/2=cosα/2*cosα/4 /sinα/4 + sinα/2 =(cosα/2*cosα/4+sinα/2*sinα/4)/sinα/4 =  cos(α/2-α/4)/sinα/4 =cosα/4/ sinα/4 =ctqα/4.