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Diketahui tan 25=p, maka tentukan nilai dari tan 245∘+tan 335∘tan 205∘−tan 115∘​

Pertanyaan

Diketahui begin mathsize 14px style tan space 25 equals p end style, maka tentukan nilai dari begin mathsize 14px style fraction numerator tan space 205 degree minus tan space 115 degree over denominator tan space 245 degree plus tan space 335 degree end fraction end style

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

jika diketahui begin mathsize 14px style tan space 25 equals p end style maka nilai dari fraction numerator tan space 205 degree minus tan space 115 degree over denominator tan space 245 degree plus tan space 335 degree end fraction equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator p squared plus 1 over denominator 1 minus p squared end fraction end cell end table

Pembahasan

Menggunakan konsep sudut berelasi di kuadran II, III, IV.

Sehingga, penyelesaiannya adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space 205 to the power of degree minus tan space 115 to the power of degree over denominator tan space 245 to the power of degree plus tan space 335 to the power of degree end fraction end cell equals cell fraction numerator tan left parenthesis 180 to the power of degree plus 25 to the power of degree right parenthesis minus tan open parentheses 90 to the power of degree plus 25 to the power of degree close parentheses over denominator tan open parentheses 270 to the power of degree minus 25 to the power of degree close parentheses plus tan open parentheses 360 to the power of degree minus 25 to the power of degree close parentheses end fraction end cell row blank equals cell fraction numerator tan space 25 to the power of degree plus text cot end text space 25 to the power of degree over denominator text cot end text space 25 to the power of degree minus tan space 25 to the power of degree end fraction end cell row blank equals cell fraction numerator p plus begin display style 1 over p end style over denominator begin display style 1 over p end style minus p end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator p squared plus 1 over denominator p end fraction end style over denominator begin display style fraction numerator 1 minus p squared over denominator p end fraction end style end fraction end cell row blank equals cell fraction numerator p squared plus 1 over denominator 1 minus p squared end fraction end cell end table end style
 

Jadi, jika diketahui begin mathsize 14px style tan space 25 equals p end style maka nilai dari fraction numerator tan space 205 degree minus tan space 115 degree over denominator tan space 245 degree plus tan space 335 degree end fraction equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator p squared plus 1 over denominator 1 minus p squared end fraction end cell end table

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