Question

Срочно,зачет за семестр,хотя-бы два номера

Answer 1

$ctg alpha = -frac{ sqrt{3} }{3}$    α∈[90°; 180°]
Табличный ctg:      α=120°
sin 2α = sin 2*120° = sin240° = sin (180° + 60°) = -sin60°
$sin 2 alpha = - frac{ sqrt{3} }{2}$


$cos ( frac{3 pi }{2} + alpha ) + sin( alpha - pi ) - tg( alpha - frac{ pi }{2} )-tg( frac{3 pi }{2} - alpha )= \ \= sin (alpha ) - sin( pi - alpha ) + tg( frac{ pi }{2}- alpha )-ctg( alpha )= \ \ =sin (alpha ) - sin(alpha ) + ctg( alpha )-ctg( alpha )= 0$


$frac{4sin alpha cos alpha cos2 alpha }{cos^22 alpha -sin^22 alpha } *ctg4 alpha = frac{2*(2sin alpha cos alpha) cos2 alpha }{cos4 alpha} *ctg4 alpha = \ \ =frac{2*sin 2alpha cos2 alpha }{cos4 alpha} *ctg4 alpha = frac{sin 4alpha}{cos4 alpha} *ctg4 alpha = \ \ = frac{sin 4alpha}{cos4 alpha} * frac{cos4 alpha }{sin4 alpha } = 1$



$1+tg alpha tg2 alpha = tg alpha *ctg alpha + tg alpha *tg2 alpha = \ \ =tg alpha *(ctg alpha +tg2 alpha )$