Equations trigonométriques - Exercices

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(InactiveHead[cos])(2 x)==-(1/(Sqrt[2]))	⟺	(InactiveHead[cos])(2 x)==(InactiveHead[cos])(((3 π)/4))
({{{, ({{2 x==((3 π)/4)+2 k π, "(1)"}, {2 x==-((3 π)/4)+2 k π, "(2)"}})}})	⟺	({{{, ({{x==((3 π)/8)+k π, "(1)"}, {x==-((3 π)/8)+k π, "(2)"}})}})	(k∈ℤ)

sin(2 x)==-((Sqrt[3])/2)	⟺	sin(2 x)==-((Sqrt[3])/2)
sin(2 x)==(InactiveHead[sin])(-(π/3))
({{{, ({{2 x==-(π/3)+2 k π, "(1)"}, {2 x==((4 π)/3)+2 k π, "(2)"}})}})	⟺	({{{, ({{x==-(π/6)+k π, "(1)"}, {x==((2 π)/3)+k π, "(2)"}})}})	(k∈ℤ)

tg((π/3)+2 x)==-(Sqrt[3])	⟺	tg((π/3)+2 x)=="tg(\!\(TraditionalForm\`\(-\(\(π\/3\)\)\)\))"
(π/3)+2 x==-(π/3)+k π	⟺	x==-(π/3)+((k π)/2)	(k∈ℤ)

(InactiveHead[cos])(x)==(InactiveHead[cos])((π/2)-2 x)
({{{, ({{"\!\(TraditionalForm\`\(x == \(\(π\/2 - \(\(2\\ x\)\)\)\)\)\) + \!\(TraditionalForm\`\(2\\ k\\ π\)\)", "(1)"}, {"\!\(TraditionalForm\`\(x == \(\(\(\(2\\ x\)\) - π\/2\)\)\)\) + \!\(TraditionalForm\`\(2\\ k\\ π\)\)", "(2)"}})}})	⟺	({{{, ({{x==(π/6)+((2 k π)/3), "(1)"}, {x==(π/2)-2 k π, "(2)"}})}})	(k∈ℤ)

x==(π/4)+k (π/2)

(InactiveHead[cos])(2 x)==(2/3)
({{{, ({{2 x==0.8410686705679303`+2 k π,  }, {2 x==0.8410686705679303`+2 k π,  }})}})

(Piecewise[{{x==0.42053433528396517`+k π,  }, {x==-0.420534+k π,  }}])

tg(3 x)==(InactiveHead[tg])(1.3258176636680326`)
3 x==1.3258176636680326` +k π
x ==  0.441939+k (π/3)