найти sin4a, если ctg2a=-2

Question

найти sin4a, если ctg2a=-2

Answer 1

sin(4α) = 2sin(2α)cos(2α) = [cos(2α)/sin(2α)] * (2sin²(2α)) = 2sin²(2α) * ctg(2α). 

1 + ctg²(2α) = (cos²(2α) + sin²(2α)) / sin²(2α) = 1/sin²(2α)); 

тогда 
sin(4α) = 2 ctg(2α) / (1 + ctg²(2α)) = 2*(−2) / (1+4) = −4/5. 

ОТВЕТ: −4/5.