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Step-by-step explanation:

[tex]\frac{sin(A+B)}{cosA.cosB} -\frac{sin(B+C)}{cosB.cosC} +\frac{sin(C+A)}{cosC.cosA} \\=\frac{sinA.cosB+sinB.cosA}{cosA.cosB} -\frac{sinB.cosC+sinC.cosB}{cosB.cosC} +\frac{sinC.cosA+sinA.cosC}{cosC.cosA} \\=\frac{sinA.cosB.cosC+sinB.cosA.cosC-sinB.cosC.cosA-sinC.cosB.cosA+sinC.cosA.cosB+sinA.cosC.cosB}{cosA.cosB.cosC} \\=\frac{2sinA.cosB.cosC}{cosA.cosB.cosC} \\=\frac{2sinA}{cosA} =2tanA[/tex]

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