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Pertanyaan

Buktikan identitas-identitas trigonometri berikut!

b. fraction numerator cos space theta over denominator sec space theta end fraction plus fraction numerator sin space theta over denominator csc space theta end fraction equals 1  

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

identitas trigonometri di atas terbukti benar.

Pembahasan

Ingat bahwa 

sec space x equals fraction numerator 1 over denominator cos space x end fraction csc space x equals fraction numerator 1 over denominator sin space x end fraction cos squared space x plus sin squared space x equals 1 

Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space theta over denominator s e c space theta end fraction plus fraction numerator sin space theta over denominator csc space theta end fraction end cell equals 1 row cell fraction numerator cos space theta over denominator begin display style fraction numerator 1 over denominator cos space theta end fraction end style end fraction plus fraction numerator sin space theta over denominator begin display style fraction numerator 1 over denominator sin space theta end fraction end style end fraction end cell equals 1 row cell cos space theta open parentheses cos space theta close parentheses plus sin space theta open parentheses sin space theta close parentheses end cell equals 1 row cell cos squared theta plus sin squared theta end cell equals 1 row 1 equals 1 end table      

Dengan demikian, identitas trigonometri di atas terbukti benar.

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