0
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That is,

I want to solve these equations below:

1

-(Sin[\[Delta]] Cos[\[Lambda]] Sin[2 \[Phi]] + 
 Sin[2 \[Delta]] Sin[\[Lambda]] Sin[\[Phi]]^2)==0

2

(Sin[\[Delta]] Cos[\[Lambda]] Sin[2 \[Phi]] - 
 Sin[2 \[Delta]] Sin[\[Lambda]] Cos[\[Phi]]^2)==0

3

-(Sin[\[Delta]] Cos[\[Lambda]] Sin[2 \[Phi]] + 
     Sin[2 \[Delta]] Sin[\[Lambda]] Sin[\[Phi]]^2)+(Sin[\[Delta]] Cos[\[Lambda]] Sin[2 \[Phi]] - 
     Sin[2 \[Delta]] Sin[\[Lambda]] Cos[\[Phi]]^2)==0

4

(Sin[\[Delta]] Cos[\[Lambda]] Cos[2 \[Phi]] + 
  1/2 Sin[2 \[Delta]] Sin[\[Lambda]] Sin[2 \[Phi]])==1

5

-(Cos[\[Delta]] Cos[\[Lambda]] Cos[\[Phi]] + 
  Cos[2 \[Delta]] Sin[\[Lambda]] Sin[\[Phi]])==0

6

-(Cos[\[Delta]] Cos[\[Lambda]] Sin[\[Phi]] - 
  Cos[2 \[Delta]] Sin[\[Lambda]] Cos[\[Phi]])==0

constraint condition:

 0 <= \[Phi] < 2 \[Pi] && 0 <= \[Delta] <= \[Pi]/2 && 
 0 <= \[Lambda] < 2 \[Pi]

solve

\[Phi], \[Delta], \[Lambda]
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0
3
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Solve[{-(Sin[δ] Cos[λ] Sin[2 ϕ]+Sin[2 δ] Sin[λ] Sin[ϕ]^2)==0,
(Sin[δ] Cos[λ] Sin[2 ϕ]-Sin[2 δ] Sin[λ] Cos[ϕ]^2)==0,
-(Sin[δ] Cos[λ] Sin[2 ϕ]+Sin[2 δ] Sin[λ] Sin[ϕ]^2)+(Sin[δ] Cos[λ] Sin[2 ϕ]-Sin[2 δ] Sin[λ] Cos[ϕ]^2)==0,
(Sin[δ] Cos[λ] Cos[2 ϕ]+1/2 Sin[2 δ] Sin[λ] Sin[2 ϕ])==1,
-(Cos[δ] Cos[λ] Cos[ϕ]+Cos[2 δ] Sin[λ] Sin[ϕ])==0,
-(Cos[δ] Cos[λ] Sin[ϕ]-Cos[2 δ] Sin[λ] Cos[ϕ])==0,
0<=ϕ<2 π, 0<=δ<=π/2, 0<=λ<2 π
},{ϕ,δ,λ},Method->Reduce]

{{ϕ->0,δ->π/2,λ->0},{ϕ->π/2,δ->π/2,λ->π},{ϕ->π,δ->π/2,λ->0},{ϕ->(3 π)/2,δ->π/2,λ->π}}

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1
  • $\begingroup$ You are very clear.Thank you very much.I was neglected the "Method->Reduce". $\endgroup$ – yonghui wang May 14 '18 at 6:58

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