task/24856782
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1) tg(π/3 -2x) ≥1
tg(π/3 -2x)≥1⇔tg(-(2x -π/3) )≥1⇔ - tg(2x -π/3)≥1⇔ tg(2x -π/3) ≤ -1 ⇔
- π/2 +πn <2x -π/3 ≤ <strong>arctg(-1) + πn ,⇔ - π/2 +πn <2x -π/3 ≤ -π/4 + πn , n<span>∈Z
-π/2 +π/3+πn <2x ≤ π/3 -π/4 + πn , n∈Z ;<br>-π/6 +πn <2x ≤ π/12 + πn , n<span>∈Z ;
- π/12 +πn/2 < x ≤ π/24 + πn /2 , n∈Z .
∪ (-π/12+πn/2 ;π/24 +πn/2)
n ∈Z
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2) √2sin(x -π/4) +1 > 0
√2sin(x -π/4) +1 > 0 ⇔ sin(x - π/4) > -1/√2 ⇔
arcsin(-1/√2) +2πn < <span>x - π/4 < </span>π - arcsin(-1/√2) +2πn ⇔
- π/4+2πn < x - π/4 < </span>π -(-π/4)+2πn ⇔ 2πn < </strong>x < 3π/2 +2πn , n∈ Z
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3₁) если cos( -π/3 - x/2) < √3 , то x - любое число <br>------------------------
3₂)наверно cos( -π/3 - x/2) < (√3)/2 ⇔ cos(-( x/2+π/3 ) ) < (√3)/2 ⇔
cos( x/2+π/3 ) < (√3)/2 ⇔
arccos( (√3)/2 ) +2πn < x/2+π/3 < 2π -arccos( (√3)/2 ) + 2πn <span>⇔
π/6 +2πn < x/2+π/3 < 2π - π/6 +2πn ⇔ -π/6 +2πn < x/2 < 3π/ 2 +2πn <span>⇔
- π/3 +4πn < x < 3π</strong> +4πn , n ∈ Z .