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Jika,  & . Tentukan nilai  !

Pertanyaan

Jika,

cos space straight A times cos space straight B plus sin space straight A times sin space straight B equals 2 over 3 & sin space straight A times sin space straight B equals 1 half.

Tentukan nilai tan space straight A times tan space straight B !

Pembahasan Soal:

Diketahui persamaan trigonometri

cos space straight A times cos space straight B plus sin space straight A times sin space straight B equals 2 over 3 dan sin space straight A times sin space straight B equals 1 half.

Substitusikan sin space straight A times sin space straight B equals 1 half ke persamaan yang lain, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight A times cos space straight B plus sin space straight A times sin space straight B end cell equals cell 2 over 3 end cell row cell cos space straight A times cos space straight B plus 1 half end cell equals cell 2 over 3 end cell row cell cos space straight A times cos space straight B end cell equals cell 1 over 6 end cell end table

Ingat bahwa tan space x equals fraction numerator sin space x over denominator cos space x end fraction maka :

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight A times tan space straight B end cell equals cell fraction numerator sin space straight A over denominator cos space straight A end fraction times fraction numerator sin space straight B over denominator cos space straight B end fraction end cell row blank equals cell fraction numerator sin space straight A times sin space straight B over denominator cos space straight A times cos space straight B end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style over denominator begin display style 1 over 6 end style end fraction end cell row blank equals cell 1 half times 6 over 1 end cell row blank equals 3 end table 

Jadi, nilai dari tan space straight A times tan space straight B equals 3.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Agustus 2021

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