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task/29523914

362. 1 )

1 - cos(π -x )+sin(π/2 +x/2) =0 ⇔1 + cos(x) +cos(x/2) =0 ⇔                                     2cos²(x/2) +cos(x/2)=0⇔ 2cos(x/2)*(cos(x/2) +1 )=0⇔[cos(x/2) =0 ; cos(x/2)= -1.

[ x/2 =π/2 +πn ; x/2  =π+2πn . ⇔[ x =π +2πn ; x  =2π+4πn , n ∈ ℤ .

362. 4 )

sin(x -π/4) +cos(x-π/4) =sin2x ⇔√2sin(x) = 2sin(x)cosx ⇔

2sin(x)*(cos(x) -(√2) /2 ) =0 ⇔  [ sin(x) =0  ; cosx =√2) /2 .

[ x =πn ; x = ±(π/4) +2πn , n ∈ ℤ .