Pertanyaan

Jika cos A 1 − sin A = p , maka nilai dari tan 2 1 A adalah ....

Jika $\frac{1 - sin A}{cos A} = p$ , maka nilai dari $tan \frac{1}{2} A$ adalah ....

$begin mathsize 14px style fraction numerator 1 minus p over denominator 1 plus p end fraction end style$
$fraction numerator size 14px 1 size 14px plus size 14px p over denominator size 14px 1 size 14px minus size 14px p end fraction$
$fraction numerator size 14px p size 14px minus size 14px 1 over denominator size 14px p size 14px plus size 14px 1 end fraction$
$fraction numerator size 14px p size 14px plus size 14px 1 over denominator size 14px p size 14px minus size 14px 1 end fraction$
$fraction numerator size 14px 1 size 14px minus size 14px p over denominator size 14px p size 14px minus size 14px 1 end fraction$

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa Maka . Jadi, jawaban yang tepat adalah A.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 minus sin invisible function application A over denominator cos invisible function application A end fraction end cell equals p row cell fraction numerator 1 minus sin invisible function application open parentheses 2 times 1 half A close parentheses over denominator cos invisible function application open parentheses 2 times 1 half A close parentheses end fraction end cell equals p row cell fraction numerator open parentheses sin squared invisible function application open parentheses 1 half A close parentheses plus cos squared invisible function application open parentheses 1 half A close parentheses close parentheses minus 2 sin invisible function application open parentheses 1 half A close parentheses cos invisible function application open parentheses 1 half A close parentheses over denominator cos squared invisible function application open parentheses 1 half A close parentheses minus sin squared invisible function application open parentheses 1 half A close parentheses end fraction end cell equals p row cell fraction numerator cos squared invisible function application open parentheses 1 half A close parentheses minus 2 sin invisible function application open parentheses 1 half A close parentheses cos invisible function application open parentheses 1 half A close parentheses plus sin squared invisible function application open parentheses 1 half A close parentheses over denominator cos squared invisible function application open parentheses 1 half A close parentheses minus sin squared invisible function application open parentheses 1 half A close parentheses end fraction end cell equals p row cell fraction numerator open parentheses cos invisible function application open parentheses 1 half A close parentheses minus sin invisible function application open parentheses 1 half A close parentheses close parentheses open parentheses cos invisible function application open parentheses 1 half A close parentheses minus sin invisible function application open parentheses 1 half A close parentheses close parentheses over denominator open parentheses cos invisible function application open parentheses 1 half A close parentheses plus sin invisible function application open parentheses 1 half A close parentheses close parentheses open parentheses cos invisible function application open parentheses 1 half A close parentheses minus sin invisible function application open parentheses 1 half A close parentheses close parentheses end fraction end cell equals p row cell fraction numerator open parentheses cos invisible function application open parentheses 1 half A close parentheses minus sin invisible function application open parentheses 1 half A close parentheses close parentheses over denominator open parentheses cos invisible function application open parentheses 1 half A close parentheses plus sin invisible function application open parentheses 1 half A close parentheses close parentheses end fraction end cell equals p row cell cos invisible function application open parentheses 1 half A close parentheses minus sin invisible function application open parentheses 1 half A close parentheses end cell equals cell p open parentheses cos invisible function application open parentheses 1 half A close parentheses plus sin invisible function application open parentheses 1 half A close parentheses close parentheses end cell row cell cos invisible function application open parentheses 1 half A close parentheses minus sin invisible function application open parentheses 1 half A close parentheses end cell equals cell p cos invisible function application open parentheses 1 half A close parentheses plus p sin invisible function application open parentheses 1 half A close parentheses end cell row cell cos invisible function application open parentheses 1 half A close parentheses minus p cos invisible function application open parentheses 1 half A close parentheses end cell equals cell sin invisible function application open parentheses 1 half A close parentheses plus p sin invisible function application open parentheses 1 half A close parentheses end cell row cell open parentheses 1 minus p close parentheses cos invisible function application open parentheses 1 half A close parentheses end cell equals cell open parentheses 1 plus p close parentheses sin invisible function application open parentheses 1 half A close parentheses end cell row cell fraction numerator 1 minus p over denominator 1 plus p end fraction end cell equals cell fraction numerator sin invisible function application open parentheses 1 half A close parentheses over denominator cos invisible function application open parentheses 1 half A close parentheses end fraction end cell row cell fraction numerator 1 minus p over denominator 1 plus p end fraction end cell equals cell tan invisible function application open parentheses 1 half A close parentheses end cell end table end style$

Maka $begin mathsize 14px style tan invisible function application open parentheses 1 half A close parentheses equals fraction numerator 1 minus p over denominator 1 plus p end fraction end style$ .

Jadi, jawaban yang tepat adalah A.