Решите уравнение sin^2x-cos2x=0.5 найдите все решение на промежутке [-(7п)/2;-2п]
Sin²x-cos2x=1/2 (1-cos2x)/2-cos2x=1/2 1-cos2x-2cos2x=1 -3cos2x=0 cos2x=0 2x=π/2+πn,n∈z x=π/4+πn/2,n∈z -7π/2≤π/4+πn/2≤-2π -14≤1+2n≤-8 -15≤2n≤-9 -7,5≤n≤-4,5 n=-7⇒x=π/4-7π/2=-13π/2 n=-6⇒x=π/4-3π=-11π/4 n=-5⇒x=π/4-5π/2=-9π/4