I was solving the trigonometric equation \(\displaystyle{{\tan}^{{2}}{x}}+{{\cot}^{{2}}{x}}={2}-{{\cos}^{{{2014}}}{\left({2}{x}\right)}}\)

Emmy Decker

Emmy Decker

Answered question

2022-04-07

I was solving the trigonometric equation
tan2x+cot2x=2cos2014(2x)

Answer & Explanation

dizzydevila6cm

dizzydevila6cm

Beginner2022-04-08Added 10 answers

The inequality proof looks fine, but if you need another way, let cosx=t, so |t|<1. The equation is then
1t2t2+t21t22+(2t21)2024=0
(2t21)2(1t2)t2+(2t21)2014=0
As both terms are non-negative, we must have 2t21=0cos2x=12

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