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Jika , maka nilai adalah

Jika begin mathsize 14px style tan space x equals 1 over t end style, maka nilai begin mathsize 14px style 2 space cos squared x space minus space 1 end style adalah begin mathsize 14px style horizontal ellipsis end style  

  1. begin mathsize 14px style fraction numerator t squared plus 1 over denominator t squared minus 1 end fraction end style 

  2. begin mathsize 14px style fraction numerator t squared over denominator t squared plus 1 end fraction end style 

  3. begin mathsize 14px style fraction numerator t squared minus 1 over denominator t squared plus 1 end fraction end style 

  4. begin mathsize 14px style fraction numerator t squared over denominator t squared minus 1 end fraction end style 

  5. begin mathsize 14px style fraction numerator 1 over denominator t squared minus 1 end fraction end style 

Jawaban:

begin mathsize 14px style tan space x equals 1 over t end style, maka sisi depan = 1 satuan dan sisi samping = t satuan

Sehingga,

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell miring squared end cell equals cell 1 squared plus t squared end cell row miring equals cell square root of 1 plus t squared end root end cell end table end style

didapat,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x end cell equals cell samping over miring end cell row blank equals cell fraction numerator t over denominator square root of 1 plus t squared end root end fraction end cell end table end style

Maka, 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 cos squared x minus 1 end cell equals cell 2 open parentheses fraction numerator t over denominator square root of 1 plus t squared end root end fraction close parentheses squared minus 1 end cell row blank equals cell 2 open parentheses fraction numerator t squared over denominator 1 plus t squared end fraction close parentheses minus 1 end cell row blank equals cell fraction numerator 2 t squared over denominator 1 plus t squared end fraction minus fraction numerator 1 plus t squared over denominator 1 plus t squared end fraction end cell row blank equals cell fraction numerator t squared minus 1 over denominator 1 plus t squared end fraction end cell row blank equals cell fraction numerator t squared minus 1 over denominator t squared plus 1 end fraction end cell end table end style

Jadi, jawaban yang tepat adalah C.

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