Tunjukkan bahwa: tan 2x=±1+ cos x1−cos x

Pertanyaan

Tunjukkan bahwa: $tan space x over 2 equals plus-or-minus square root of fraction numerator 1 minus cos space x over denominator 1 plus space cos space x end fraction end root$

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Pembahasan

Untuk membuktikan rumus sudut paruh tangen, kita dapat menggunakan rumus sudut paruh sinus dan cosinus:

$sin space x over 2 equals plus-or-minus square root of fraction numerator 1 minus cos space x over denominator 2 end fraction end root cos space x over 2 equals plus-or-minus square root of fraction numerator 1 plus cos space x over denominator 2 end fraction end root$

Seperti yang kita ketahui bahwa:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x end cell equals cell fraction numerator sin space x over denominator cos space x end fraction end cell row cell tan space 1 half x end cell equals cell fraction numerator sin space begin display style 1 half end style x over denominator cos space begin display style 1 half end style x end fraction end cell row cell tan space 1 half x end cell equals cell fraction numerator plus-or-minus square root of begin display style fraction numerator 1 minus cos space x over denominator 2 end fraction end style end root over denominator plus-or-minus square root of begin display style fraction numerator 1 plus cos space x over denominator 2 end fraction end style end root end fraction end cell row cell tan space 1 half x end cell equals cell plus-or-minus fraction numerator square root of 1 minus cos space x end root over denominator square root of 1 plus cos space x end root end fraction end cell end table$

Terbukti bahwa: $tan space x over 2 equals plus-or-minus square root of fraction numerator 1 minus cos space x over denominator 1 plus space cos space x end fraction end root$ .