5sin^{2} x - 3,5sinx cosx + 2cos^{2} x = 3

Question

5sin^{2} x - 3,5sinx cosx + 2cos^{2} x = 3

Answer 1

                                             Решение:

 

5sin^2x-3,5sinxcosx+2cos^2x-3sin^2x-3cos^2x=0
2sin^2x-cos^2x-3,5sinxcosx=0
2tg^x-3,5tgx-1=0
tgx=-1/4
tgx=2
x=arctg2+Пk
x=-arctg(1/4)+Пk.