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determinant-Solve-the-following-Equation-81-sin-2-x-81-cos-2-x-30-

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Question Number 134464 by bramlexs22 last updated on 04/Mar/21
determinant (((Solve the following Equation)),(( 81^(sin^2 x) + 81^(cos^2 x) = 30 )))
SolvethefollowingEquation81sin2x+81cos2x=30
Commented by harckinwunmy last updated on 04/Mar/21
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Answered by EDWIN88 last updated on 04/Mar/21
81^(sin^2 x) + 81^(1−sin^2 x) = 30 multiply both sides by 81^(sin^2 x) (81^(sin^2 x) )^2 −30×81^(sin^2 x) + 81 = 0 let 81^(sin^2 x) = u ⇒u^2 −30u + 81 = 0 (u−3)(u−27) = 0 for u=3 → determinant (((81^(sin^2 x) = 3 ⇒sin^2 x=(1/4))),((sin x=(1/2) or sin x=−(1/2))),((x= { ((π/6)),((5π/6)) :}+ 2kπ or x= { ((−π/6)),((7π/6)) :}+2kπ))) for u=27→ determinant (((81^(sin^2 x) =27⇒sin^2 x=(3/4))),((sin x = ((√3)/2) or sin x=−((√3)/2))),((x= { ((π/3)),((2π/3)) :}+2kπ or x= { ((−π/3)),((4π/3)) :}+2kπ)))
81sin2x+811−sin2x=30multiplybothsidesby81sin2x(81sin2x)2−30×81sin2x+81=0let81sin2x=u⇒u2−30u+81=0(u−3)(u−27)=0foru=3→81sin2x=3⇒sin2x=14sinx=12orsinx=−12x={π/65π/6+2kπorx={−π/67π/6+2kπforu=27→81sin2x=27⇒sin2x=34sinx=32orsinx=−32x={π/32π/3+2kπorx={−π/34π/3+2kπ

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