Task/28187627
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1.
* * * sinx = a , |a| ≤1 ⇒ x = (-1)ⁿ.arcsina + πn ,n ∈ ℤ * * *
sinx = - √2 /2 ⇒ x = (-1)ⁿ.(-π/4) + πn ,n ∈ ℤ ⇔ x = (-1)ⁿ⁺¹(π/4) + πn ,n ∈ ℤ .
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2.
* * * cosx = a , |a| ≤1 ⇒ x = ±arccosa + 2πn ,n ∈ ℤ * * *
cosx = - √2 /2 ⇒ x = ± 3π/4 +2πn , n ∈ ℤ .
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3.
* * * tgx = a ⇒ x = arctga + πn ,n ∈ ℤ * * *
tgx = 1 ⇒ x = π/4 + πn ,n ∈ ℤ .
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4. * * * cos2x = cos²x - sin²x = 2cos²x -1 ⇒ cos²x = (1+cos2x) / 2 * * *
cos²x =1/2 ⇔ (1+cos2x) / 2 =1/2 ⇔ cos2x=0 ⇒ 2x =π/2+πn ,n∈Z ⇔
x =π/4 + (π/2).n , n∈Z .