Roboguru

Pertanyaan

tan open parentheses x close parentheses minus cot open parentheses straight x close parentheses

  1. fraction numerator 1 plus 2 space cos squared space x over denominator sin space x cross times cos space x end fraction 

  2. fraction numerator 1 minus 2 space cos squared space x over denominator sin space x cross times cos space x end fraction 

  3. fraction numerator 1 minus 2 space cot squared space x over denominator sin space x cross times cos space x end fraction 

  4. fraction numerator 1 minus 2 space cos squared space x over denominator sin space x cross times cot space x end fraction 

  5. fraction numerator 1 minus 2 space cos squared space x over denominator sin space x cross times cos space x end fraction

Pembahasan Soal:

Diketahui tan open parentheses x close parentheses minus cot open parentheses straight x close parentheses

Dengan menggunakan identitas trigonometri:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared x plus cos squared x end cell equals 1 row cell sin squared x end cell equals cell 1 minus cos squared x end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell tan open parentheses x close parentheses minus cot open parentheses straight x close parentheses end cell equals cell fraction numerator sin space x over denominator cos space x end fraction minus fraction numerator cos space x over denominator sin space x end fraction end cell row blank equals cell fraction numerator sin space x space left parenthesis sin space x right parenthesis over denominator cos space x space left parenthesis cos space x right parenthesis end fraction minus fraction numerator cos space x space left parenthesis cos space x right parenthesis over denominator sin space x space left parenthesis cos space x right parenthesis end fraction end cell row blank equals cell fraction numerator sin squared x minus cos squared x over denominator sin space x cross times cos space x end fraction end cell row blank equals cell fraction numerator 1 minus cos squared x minus cos squared x over denominator sin space x cross times cos space x end fraction end cell row blank equals cell fraction numerator 1 minus 2 cos squared x over denominator sin space x cross times cos space x end fraction end cell end table

Dengan demikian, tan open parentheses x close parentheses minus cot open parentheses straight x close parentheses adalah fraction numerator 1 minus 2 space cos squared space x over denominator sin space x cross times cos space x end fraction.

Oleh karena itu, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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