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In[7]:= Simplifyx2
x2 + y2 + z2+
z2 x2
x2 + y2 + z22x2 + y2
+y2
x2 (x + y)2
Out[7]=y2
x2 (x + y)2+
x2 x2 + y2 + 1 +1
x2+y2 z2
(x2 + y2 + z2)2
In[8]:= M = {{Sin[θ] Cos[ϕ], Sin[θ] Sin[ϕ], Cos[θ]},{Cos[θ] Cos[ϕ], Cos[θ] Sin[ϕ], -Sin[θ]},{-Sin[ϕ], Cos[ϕ], 0}}
Out[8]= {{Cos[ϕ] Sin[θ], Sin[θ] Sin[ϕ], Cos[θ]},{Cos[θ] Cos[ϕ], Cos[θ] Sin[ϕ], -Sin[θ]}, {-Sin[ϕ], Cos[ϕ], 0}}
In[12]:=
MatrixForm[M]
Out[12]//MatrixForm=Cos[ϕ] Sin[θ] Sin[θ] Sin[ϕ] Cos[θ]Cos[θ] Cos[ϕ] Cos[θ] Sin[ϕ] -Sin[θ]
-Sin[ϕ] Cos[ϕ] 0
In[10]:=
FullSimplify[Inverse[M]]
Out[10]= {{Cos[ϕ] Sin[θ], Cos[θ] Cos[ϕ], -Sin[ϕ]},{Sin[θ] Sin[ϕ], Cos[θ] Sin[ϕ], Cos[ϕ]}, {Cos[θ], -Sin[θ], 0}}
In[11]:=
MatrixForm[%]
Out[11]//MatrixForm=Cos[ϕ] Sin[θ] Cos[θ] Cos[ϕ] -Sin[ϕ]Sin[θ] Sin[ϕ] Cos[θ] Sin[ϕ] Cos[ϕ]
Cos[θ] -Sin[θ] 0