Math

Prove that (cos2A)÷ ( 1+sin2A) = (cotA -1) ÷ (cotA +1)

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  1. The trick here is to recall that 1 = cos^a+sin^2A

    cos2A/(1+sin2A)
    (cos^2A-sin^2A)/(1+2sinAcosA)
    (cos^2A-sin^2A)/(cos^2A+2sinAcosA+sin^2A)
    (cosA+sinA)(cosA-sinA)/(cosA+sinA)^2
    (cosA-sinA)/(cosA+sinA)
    (cotA-1)/(cotA+1)

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  2. The trick here is to recall that 1 = cos^a+sin^2A

    cos2A/(1+sin2A)
    (cos^2A-sin^2A)/(1+2sinAcosA)
    (cos^2A-sin^2A)/(cos^2A+2sinAcosA+sin^2A)
    (cosA+sinA)(cosA-sinA)/(cosA+sinA)^2
    (cosA-sinA)/(cosA+sinA)
    (cotA-1)/(cotA+1)

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