Wolfram Cloud Document

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$Version

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12.3.0 for Microsoft Windows (64-bit) (May 10, 2021)

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X=Rationalize[1.9066,0];Y=Rationalize[-0.09122,0];Z=Rationalize[-0.43421,0];R=Rationalize[1.95756,0];

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Reduce[{X*(((Cos[c])*(Cos[b]))-(Cos[b])*(Sin[a])*(Sin[c]))+Y*((Cos[c])*(Sin[a])+(Cos[a])*(Cos[b])*(Sin[c]))+Z*(Sin[c]*(Sin[b]))==0,X*((-Sin[c])*(Cos[a])-(Cos[b])*(Sin[a])*(Cos[c]))+Y*((-Sin[c])*(Sin[a])+(Cos[b])*(Cos[a])*(Cos[c]))+Z*(Cos[c]Sin[b])==0,(X*Sin[b]*Sin[a]-Y*Sin[b]*Cos[a]+Z*Cos[b])==R},{a,b,c}]

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Solve[{X*(((Cos[c])*(Cos[b]))-(Cos[b])*(Sin[a])*(Sin[c]))+Y*((Cos[c])*(Sin[a])+(Cos[a])*(Cos[b])*(Sin[c]))+Z*(Sin[c]*(Sin[b]))==0,X*((-Sin[c])*(Cos[a])-(Cos[b])*(Sin[a])*(Cos[c]))+Y*((-Sin[c])*(Sin[a])+(Cos[b])*(Cos[a])*(Cos[c]))+Z*(Cos[c]Sin[b])==0,(X*Sin[b]*Sin[a]-Y*Sin[b]*Cos[a]+Z*Cos[b])==R},{a,b,c}]

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