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fand
@fand
July 2022
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16 ^sin квадрат х+ 16^cos квадрат х=10
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sedinalana
Verified answer
16^sin²x+16^(1-sin²x)-10=0
16^sin²x+16/(16^sin²x)-10=0
16^2sin²x-10*16^sin²x+16=0
16^sin²x=a
a²-10a+16=0
a1+a2=10 U a1*a2=16
a1=2⇒16^sin²x=2
2^4sin²x=2
4sin²x=1
sin²x=1/4
sinx=+-1/2
x=+-π/6+2πn,n∈z
a2=8⇒16^sin²x=8
2^4sin²x=2³
4sin²x=3
sin²x=3/4
sinx=+-√3/2
x=+-π/3+2πk,k∈z
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Verified answer
16^sin²x+16^(1-sin²x)-10=016^sin²x+16/(16^sin²x)-10=0
16^2sin²x-10*16^sin²x+16=0
16^sin²x=a
a²-10a+16=0
a1+a2=10 U a1*a2=16
a1=2⇒16^sin²x=2
2^4sin²x=2
4sin²x=1
sin²x=1/4
sinx=+-1/2
x=+-π/6+2πn,n∈z
a2=8⇒16^sin²x=8
2^4sin²x=2³
4sin²x=3
sin²x=3/4
sinx=+-√3/2
x=+-π/3+2πk,k∈z