Inverse Fourier transform of $\sin^{2} $

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Maybe my question is stupid but why the Fourier transform of $ \DeclareMathOperator{\tri}{tri}\sin (f T \pi ) ^{2} $ isn’t $ \frac{1}{T \pi } \tri \big( \frac{t}{T \pi } \big) $ ? if I write the sin function as a cosine , I obtain the same result of my book , but why is this wrong ? Tri is triangular impulse