As relações secante, cossecante e cotangente são funções bem definidas, respectivamente para s e n left parenthesis x right parenthesis not equal t...

As relações secante, cossecante e cotangente são funções bem definidas, respectivamente para s e n left parenthesis x right parenthesis not equal to space 0 comma cos left parenthesis x right parenthesis not equal to space 0. Para resolver equações envolvendo as funções secante, cossecante e cotangente, basta reduzi-las em função de seno e cosseno. O conjunto solução da equação s e c left parenthesis x right parenthesis equals s e c left parenthesis begin inline style fraction numerator 2 straight pi over denominator 3 end fraction end style right parenthesis é: a. S equals x element of R semicolon x equals negative begin inline style fraction numerator 2 straight pi over denominator 3 end fraction end style plus 2 k pi comma k element of straight integer numbers. b. S equals left curly bracket x element of R semicolon x equals begin inline style fraction numerator 2 straight pi over denominator 3 end fraction end style plus k pi space o u space x equals begin inline style straight pi over 3 end style plus k pi comma k element of straight integer numbers right curly bracket. c. S equals left curly bracket x element of R semicolon space x equals begin inline style plus-or-minus fraction numerator 2 pi over denominator 3 end fraction end style plus 2 k pi comma k element of straight integer numbers right curly bracket. d. S equals left curly bracket x element of R semicolon x equals begin inline style fraction numerator 2 straight pi over denominator 3 end fraction end style plus 2 k pi o u x equals begin inline style straight pi over 3 end style plus 2 k pi comma k element of R right curly bracket. e. S equals left curly bracket x element of R semicolon x equals begin inline style fraction numerator 2 straight pi over denominator 3 end fraction end style plus 2 k pi comma k element of R right curly bracket.