2cos²x-7sin-5=0

2sinx-3cosx=0

1) 2-2sin²x-7sinx-5=0

2sin²x+7sinx+3=0

sinx=a

2a²+7a+3=0

D=49-24=25

a1 = (-7-5) / 4=-3⇒sinx=-3∉[-1; 1] нет решения

a2 = (-7+5) / 4=-1/2⇒sinx=-1/2⇒x = (-1) ^n+1 * π/6+πn

2) 4sinx/2cosx/2-3cos²x/2+3sin²x/2=0 / cos²x/2≠0

3tg²x/2+4tgx/2-3=0

tgx/2=a

3a²+4a-3=0

D=16+36=52

a1 = (-4-2√13) / 6 = (-2-√13) / 3⇒tgx/2 = (-2-√13) / 3⇒x/2=arctg (-2-√13) / 3+πn⇒x=

=2arctg (-2-√13) / 3+2πn

a2 = (-2+√13) / 3⇒tgx/2 = (-2+√13) / 3+πn⇒x=2arctg (-2+√13) / 3+2πn