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tanA = sinA/cosA
cotA = cosA/sinA
tanA / (1 + tan^2A)^2 = sinA/cosA / (cos^2A/cos^2A + sin^2A/cos^2A)^2 = sinA/cosA / ((cos^2A + sin^2A) / cos^2A)^2 = sinA/cosA / (1 / cos^2A)^2 = sinA/cosA * cos^4A = sinAcos^3A
cotA / (1 + cot^2A)^2 = cosA/sinA / (sin^2A/sin^2A + cos^2A / sin^2A)^2 = cosA/sinA / ((sin^2A + cos^2A) / sin^2A)^2 = cosA/sinA / (1 / sin^2A)^2 = cosA/sinA * sin^4A = cosAsin^3A
tanA / (1 + tan^2A)^2 + cotA / (1 + cot^2A)^2 = sinAcos^3A + sin^3Acos^A = sinAcosA(cos^2A + sin^2A) = sinAcosA
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