1/Tan3A−Tana − 1/Cot3A−Cota=Kcot2A, Then K Is Equal To

Given

[latex] \frac{1}{tan3A – tan A} – \frac{1}{cot3A – cot A} = k cot2A[/latex]

LHS = [latex] \frac{1}{\frac{sin3A}{cos3A}- \frac{sinA}{cosA}} – \frac{1}{\frac{cos3A}{sin3A}- \frac{cosA}{sinA}} [/latex]

= [latex] \frac{cos3AcosA}{sin2A} + \frac{sin3AsinA}{sin2A} [/latex]

= cot2A

Therefore, K = 1

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