Question

Решите уравнение:

а)3(cos^2)x +1/2sinx=2

б)2(sin^2)x - 5sinx*cosx-(cos^2)x=-2

Answer 1

a) 3cos^2x+1/2-1/2cos^2x=2

2.5cos^2x=1,5

cos^2x=0,6

1+cos2x=1,2

cos2x=0,2

2x=+/-arccos0,2+2pn

x=+/-arccos0,2/2+pn

b)2tg^2x-5tgx+1=0

2a^2-5a+1=0

d=25-8=17

a1,2=5+/-sgrt17/4

[tgx=1,25+sgrt17/4 [x=arctg1,25+sgrt17/4  +pn

[tgx=1,25-sgrt17/4  [x=arctg1,25-sgrt17/4  + pn