Question

4sinx-3cosx=5
решмте пожалуйстаа

Answer 1

$4sinx-3cosx=5\\ frac{4*2tg(x/2)}{1+tg^2(x/2)}- frac{3(1-tg^2(x/2)}{1+tg^2(x/2)}=5|*(1+tg^2(x/2))\\8tg(x/2)-3+3tg^2(x/2)=5+5tg^2(x/2)\2tg^2(x/2)-8tg(x/2)+8=0|:2\ tg^2(x/2)-4tg(x/2)+4=0\t=tg(x/2)\t^2-4t+4=0\D=(-4)^2-4*1*4=16-16=0\tg(x/2)=0\x/2= pi n, nin Z\x=2 pi n, nin Z$