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tan^−1[acosx−bsinx/bcosx+asinx]
=tan^−1[acosx/bcosx−bsinx/bcosx]÷[bcosx/bcosx+asinx/bcosx]
=tan^−1[a/b−tanx]÷[1+a/b × tanx]
=tan^−1[tanα−tanx÷1+tanα×tanx]
,
where a/b=tanα
=tan^−1[tan(α−x)]
=α−x
=tan^−1(a/b)−x
hope it's helpful
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