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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