Solve this trigonometric equation \(\displaystyle{\left\lbrace{\tan}^{{2}}\right\rbrace}{x}+{\left\lbrace{\cot}^{{2}}\right\rbrace}{x}-{3}{\left({\tan{{x}}}-{\cot{{x}}}\right)}={0}\)

Oxinailelpels3t14

Oxinailelpels3t14

Answered question

2022-03-20

Solve this trigonometric equation {tan2}x+{cot2}x3(tanxcotx)=0

Answer & Explanation

Marcos Boyer

Marcos Boyer

Beginner2022-03-21Added 12 answers

Let tanxcotx=t
Thus,
t2+23t=0
For t=1 we obtain
tan2xtan{x}1=0
which gives x=arctan1±52+πk, where kZ
For t=2 we obtain
tan2x2tan{x}1=0
which gives x=arctan(1±2)+πk, where kZ
Actually, arctan(1+2)=3π8 and arctan(12)=π8

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