If θ is an acute angle and cot θ + tan θ = 2, then find the value of $$\tan^{12}{\theta}+\cot^{12}{\theta}+2\tan^5{\theta}\cot^7{\theta}.$$​

Correct option is A

Given:
tanθ + cotθ = 2
Solution:

Put the value of θ= 45°,
tan45° = 1, and cot45° = 1
then, tanθ+ cotθ = 2
tan45° + cot45° = 2 $$\implies$$​1+1=2

$$\tan^{12}{\theta}+\cot^{12}{\theta}+2\tan^5{\theta}\cot^7{\theta}. \\\tan^{12}45° + \cot^{12}45°+2tan^545°cot^745°\\1^{12} +1^{12}+2\times1^51^7 = 4$$

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