Question

дано: cos a= 5/13,        0<a<pi/2 найдите sin 2a

Answer 1

  т.к 0<a<pi/2, sin a>0, cos a>0

 

$sin a = sqrt(1-cos a^{2}) = sqrt(1-5/13^{2}) = sqrt(1-25/169) = sqrt(144/169) = 12/13 cos a = 5/13$

cos a = 5/13

 

 

 

 

sin 2a = 2 sin a cos a = 2*(5/13*12/13) = 120/169 

Ответ: sin 2a = 120/169