А -2sin(3x-π/4)=-√2 sin(3x-π/4)=√2/2 [3x-π/4=π/4+2πk⇒3x=π/2+2πk⇒x=π/6+2πk/3,k∈z [3x-π/4=3π/4+2πk⇒3x=π+2πk⇒x=π/3+2πk/3,k∈z б 2(1-cos²x)+5cosx-5=0 2-2cos²x+5cosx-5=0 cosx=a 2a²-5a+3=0 D=25-24=1 a1=(5-1)/4=1⇒cosx=1⇒x=2πk,k∈z a2=(5+1)/2=1,5⇒cosx=1,5>1 нет решения в 4sin²x/2-3cosx/2*sinx/2-cos²x/2=0 делим на cos²x/2 4tg²x/2-3tgx/2-1=0 tgx/2=a 4a²-3a-1=0 D=9+16=25 a1=(3+5)/8=1⇒tgx/2=1⇒x/2=π/4+πk⇒x=π/2+2πk a2=(3-5)/8=-1/4⇒tgx/2=-1/4⇒x/2=-arctg0,25+πk⇒x=-2arctg0,25+2πk,k∈z
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А-2sin(3x-π/4)=-√2
sin(3x-π/4)=√2/2
[3x-π/4=π/4+2πk⇒3x=π/2+2πk⇒x=π/6+2πk/3,k∈z
[3x-π/4=3π/4+2πk⇒3x=π+2πk⇒x=π/3+2πk/3,k∈z
б
2(1-cos²x)+5cosx-5=0
2-2cos²x+5cosx-5=0
cosx=a
2a²-5a+3=0
D=25-24=1
a1=(5-1)/4=1⇒cosx=1⇒x=2πk,k∈z
a2=(5+1)/2=1,5⇒cosx=1,5>1 нет решения
в
4sin²x/2-3cosx/2*sinx/2-cos²x/2=0 делим на cos²x/2
4tg²x/2-3tgx/2-1=0
tgx/2=a
4a²-3a-1=0
D=9+16=25
a1=(3+5)/8=1⇒tgx/2=1⇒x/2=π/4+πk⇒x=π/2+2πk
a2=(3-5)/8=-1/4⇒tgx/2=-1/4⇒x/2=-arctg0,25+πk⇒x=-2arctg0,25+2πk,k∈z