Prove that sin2X.tanX + cos2X.cotX + 2sinXCosX = tanX + cotX = secX.cosecX
\( tan θ + cot θ = \dfrac{sin θ}{cos θ} + \dfrac{cos θ}{sin θ} \\ \dfrac{sin^2 θ + cos^2 θ}{sin θ cos θ} = \dfrac{1}{sin θ cos θ} \\ sec θ × cosec θ \)
\( tan θ + cot θ = \dfrac{sin θ}{cos θ} + \dfrac{cos θ}{sin θ} \\ \dfrac{sin^2 θ + cos^2 θ}{sin θ cos θ} = \dfrac{1}{sin θ cos θ} \\ sec θ × cosec θ \)