Pertanyaan

Jika tan 3 5 ∘ = p , maka nilai dari tan 21 5 ∘ − tan 30 5 ∘ tan 5 5 ∘ + tan 14 5 ∘ adalah ....

Jika $tan 3 5^{\circ} = p,$ maka nilai dari $\frac{tan 5 5 ^{\circ} + tan 14 5 ^{\circ}}{tan 21 5 ^{\circ} - tan 30 5 ^{\circ}}$ adalah .... $\;$

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

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Jawaban terverifikasi

Pembahasan

Perhatikan perhitungan berikut! Jadi, jawaban yang tepat adalah B.

Perhatikan perhitungan berikut!

$begin mathsize 14px style fraction numerator tan invisible function application 55 degree plus tan invisible function application 145 degree over denominator tan invisible function application 215 degree minus tan invisible function application 305 degree end fraction equals fraction numerator tan invisible function application left parenthesis 90 degree minus 35 degree right parenthesis plus tan invisible function application left parenthesis 180 degree minus 35 degree right parenthesis over denominator tan invisible function application left parenthesis 180 degree plus 35 degree right parenthesis minus tan invisible function application left parenthesis 270 degree plus 35 degree right parenthesis end fraction equals fraction numerator cot invisible function application 35 degree plus left parenthesis negative tan invisible function application 35 degree right parenthesis over denominator tan invisible function application 35 degree minus left parenthesis negative cot invisible function application 35 degree right parenthesis end fraction equals fraction numerator cot invisible function application 35 degree minus tan invisible function application 35 degree over denominator tan invisible function application 35 degree plus cot invisible function application 35 degree end fraction equals fraction numerator fraction numerator 1 over denominator tan invisible function application 35 degree end fraction minus tan invisible function application 35 degree over denominator tan invisible function application 35 degree plus fraction numerator 1 over denominator tan invisible function application 35 degree end fraction end fraction equals fraction numerator 1 over p minus p over denominator p plus 1 over p end fraction equals fraction numerator 1 over p minus p over denominator p plus 1 over p end fraction times p over p equals fraction numerator 1 minus p squared over denominator p squared plus 1 end fraction end style$

Jadi, jawaban yang tepat adalah B.