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1) a) $\sqrt{3} · \frac{ \sqrt{3} }{2} + \frac{1}{2} · \frac{1}{2} - 1 ·(-1) +0 = = 3/2+1/4+1 = 11/4 =[tex]2 \frac{3}{4} ;$

б) 1/2 - $\sqrt{2} · \frac{ \sqrt{2} }{2} + \sqrt{3} · \sqrt{3} = \frac{1}{2} -1+3 = 2 \frac{1}{2}$

2) а) = $\frac{1 - сos^{2} \alpha }{sin \alpha } = \frac{ cos^{2} \alpha + sin^{2} \alpha- cos^{2} \alpha }{sin \alpha } = sin[tex] \alpha$ ;
b) sin $\alpha - cos \alpha - sin \alpha +cos \alpha =0;$
3) a) $= xsin{2} \alpha +2sin \alpha ·cos \alpha + cos^{2} \alpha - 2sin \alpha cos \alpha = sin^{2} \alpha + cos^{2} \alpha =1;$
b) tg $\alpha +ctg \alpha = \frac{sin \alpha }{cos \alpha } + \frac{cos \alpha }{sin \alpha } = \frac{ sin^{2} \alpha + cos^{2} \alpha }{sin \alpha } = \frac{1}{0,4}$ =2,5.
4) $1+ ctg^{2} \alpha = \frac{1}{ sin^{2} \alpha } ; 1+ \frac{25}{144} = \frac{1}{ sin^{2} \alpha }; \frac{169}{144} = \frac{1}{ sin^{2} \alpha }$
$sin \alpha = - \frac{12}{13}; sin^{2} \alpha + cos^{2} \alpha =1; cos^{2} \alpha =1 - sin^{2} \alpha ; cos \alpha = \sqrt{1 - sin^{2} \alpha }$ $= \sqrt{1 - \frac{144}{169} } = \sqrt{ \frac{25}{169} } ; cos \alpha = -\frac{5}{13} tg[tex] \alpha= \frac{sin \alpha }{cos \alpha } = \frac{(- \frac{12}{13} )}{(- \frac{5}{y13} )} = \frac{12}{5}$

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