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 .