Question

tanA +cotA=2. find tan(power)3+7(cot)(power)3​

Answer 1

Required answer = 8.

Refer to the above attachment.

Answer 2

Answer: 8

Step-by-step explanation:

$\tan{A}+\cot{A} = 2 \\ \\ \tan{A} + \frac{1}{\tan{A}} = 2 \\ \\ \text{We know that (Assuming each term is positive): } \text{AM} \ge \text{GM} \\ \\ \text{i.e: } \tan{A} + \frac{1}{\tan{A}} \ge 2 \times \tan{A} \times \frac{1}{\tan{A}} \\ \\ \text{For Equality:} \tan{A} = \frac{1}{\tan{A}} = 1 \\ \\ \text{Therefore: } A\ = \ 45^{\circ} \\ \\ \text{Substituting In the equation We get:} \\ \\ \tan{A}^3 + 7\cot{A}^3 = 1 + 7 = 8$

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