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Hi Tutors...hope you are having a great day! I managed to find values for delta but could not show solution to equation.

Regards and thanks.

 May 7, 2019
 #1
avatar+26396 
+4

Trigonometry

 

tanθ=λ tan(Aθ)tanθ=sin(θ)cos(θ)tan(Aθ)=sin(Aθ)cos(Aθ)sin(θ)cos(θ)=λ (sin(Aθ)cos(Aθ))sin(Aθ)=sin(A)cos(θ)cos(A)sin(θ)cos(Aθ)=cos(A)cos(θ)+sin(A)sin(θ)sin(θ)cos(θ)=λ (sin(A)cos(θ)cos(A)sin(θ)cos(A)cos(θ)+sin(A)sin(θ))sin(θ)(cos(A)cos(θ)+sin(A)sin(θ))=λ cos(θ)(sin(A)cos(θ)cos(A)sin(θ))cos(A)sin(θ)cos(θ)+sin(A)sin2(θ)=λ cos2(θ)sin(A)λ cos(A)sin(θ)cos(θ)(λ+1)cos(A)sin(θ)cos(θ)=λ cos2(θ)sin(A)sin(A)sin2(θ)cos2(θ)=1sin2(θ)(λ+1)cos(A)sin(θ)cos(θ)=λ (1sin2(θ))sin(A)sin(A)sin2(θ)(λ+1)cos(A)sin(θ)cos(θ)=λ sin(A)(λ+1)sin(A)sin2(θ)(λ+1)cos(A)sin(θ)cos(θ)+(λ+1)sin(A)sin2(θ)=λ sin(A)(λ+1)(cos(A)sin(θ)cos(θ)+sin(A)sin2(θ))=λ sin(A)sin(θ)cos(θ)=sin(2θ)2sin2(θ)=1cos(2θ)2(λ+1)(cos(A)sin(2θ)2+sin(A)(1cos(2θ)2))=λ sin(A)(λ+1)(cos(A)sin(2θ)+sin(A)(1cos(2θ)))=2λ sin(A)(λ+1)(cos(A)sin(2θ)sin(A)cos(2θ)+sin(A))=2λ sin(A)cos(A)sin(2θ)sin(A)cos(2θ)=sin(2θA)(λ+1)(sin(2θA)+sin(A))=2λ sin(A)(λ+1)sin(2θA)+(λ+1)sin(A)=2λ sin(A)(λ+1)sin(2θA)=2λ sin(A)(λ+1)sin(A)(λ+1)sin(2θA)=2λ sin(A)λ sin(A)sin(A)(λ+1)sin(2θA)=λ sin(A)sin(A)(λ+1)sin(2θA)=(λ1)sin(A)(λ1)sin(A)=(λ+1)sin(2θA)

 

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 May 7, 2019
 #2
avatar+118703 
+2

Very impressive Heureka    laugh

Melody  May 7, 2019
 #4
avatar+26396 
+3

Thank you, Melody !

 

laugh

heureka  May 7, 2019
 #3
avatar+26396 
+3

 Trigonometry

 

tanθ=2 tan(60θ)|λ=2, A=60(21)sin60=(2+1)sin(2θ60)sin60=3sin(2θ60)|sin(60)=3232=3sin(2θ60)sin(2θ60)=362θ60=arcsin(36)+360n, nZ2θ=60+16.7786548810+360n2θ=76.7786548810+360nθ=38.3893274405+180nθ1=38.3893274405θ2=38.3893274405+180θ2=218.389327440sin(2θ60)=sin(180(2θ60))=sin(1802θ+60)=sin(2402θ)sin(2402θ)=362402θ=arcsin(36)+360n, nZ2θ=24016.7786548810360n2θ=223.221345119360nθ=111.610672560180nθ3=111.610672560θ4=111.610672560+180θ4=291.610672560

 

 

laugh

 May 7, 2019
 #5
avatar+239 
+1

Great job Heureka! and mostly thanks for your clarifications (boxed) to support the solution flow! As they say in Italy you know one more than the devil!

 May 8, 2019
 #6
avatar+26396 
+1

Thank you, OldTimer !

 

laugh

heureka  May 8, 2019

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