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Question Number 211115 by Durganand last updated on 28/Aug/24

Answered by som(math1967) last updated on 28/Aug/24

$$tanA+2tan2A+\frac{4}{tan2.2A}$$$$=tanA+2tan2A+\frac{4(1-{tan}^{2}2A)}{2tan2A}$$$$=tanA+\frac{2{tan}^{2}2A+2-2{tan}^{2}2A}{tan2A}$$$$=tanA+\frac{2}{tan2A}$$$$=tanA+\frac{(1-{tan}^{2}A)}{tanA}$$$$=\frac{{tan}^{2}A+1-{tan}^{2}A}{tanA}$$$$=\frac{1}{tanA}=cotA$$$$$$

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