Prove that: $\dfrac{1 + cos2A}{sin2A} = cotA$.

Solution:

LHS

$= \dfrac{1 + cos2A}{sin2A}$

Use Trigonometry Identity of 1 and multiple angle formula of cos2A, we get,

$= \dfrac{(sin²A+cos²A)+(cos²A - sin²A)}{sin2A}$

$= \dfrac{sin²A + cos²A + cos²A - sin²A}{sin2A}$

$= \dfrac{2cos²A}{sin2A}$

$= \dfrac{2cos²A}{2sinAcosA}$

$= \dfrac{2×cosA×cosA}{2×sinA×cosA}$

$= \dfrac{cosA}{sinA}$

$= cotA$

RHS

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