34sinx=cosx

(2cos^2) x=1-sinx

2sin4x - (2sin^2) x=1

1) 34sinx-cosx=0/cosx

34tgx-1=0

tgx=1/34

x=arctg1/34+πn, n∈z

2) 2-2sin²x-1+sinx=0

sinx=a

2a²-a-1=0

D=1+8=9

a1 = (1-3) / 4=-1/2⇒sinx=-1/2⇒x = (-1) ^ (n+1) * π/6+πn, n∈z

a2 = (1+3) / 4=1⇒sinx=1⇒x=π/2+2πk, k∈z

3) 4sinxcosx-2sin²x-sin²x-cos²x=0/cos²x

3tg²x-4tgx+1=0

tgx=a

3a²-4a+1=0

D=16-12=4

a1 = (4-2) / 6=1/3⇒tgx=1/3⇒x=arctg1/3+πn, n∈z

a2 = (4+2) / 6=1⇒tgx=1⇒x=π/4+πk, k∈z