Complementary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> violation induced by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi><

In this Letter, we demonstrate that <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>T</a:mi></a:math>-odd and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>T</c:mi></c:math>-even correlations, with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>T</e:mi></e:math> representing time reversal, when satisfying specific conditions, result, respectively, in cosine and sine strong phase dependencies of the corresponding <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>C</g:mi><g:mi>P</g:mi></g:math> violation. Additionally, we identify pairs of these <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math> violation observables in hadron decays depend on precisely the same strong phases within the helicity amplitude scheme. This complementarity could reduce the strong phase reliance in the study of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>C</k:mi><k:mi>P</k:mi></k:math> violation while also mitigating the risk of suppressed <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>C</m:mi><m:mi>P</m:mi></m:math> violation due to exceptionally small strong phases. Moreover, our proposal holds broad application prospects in further investigating <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>C</o:mi><o:mi>P</o:mi></o:math> violation in baryon decays, which has recently been discovered in the LHCb experiment.