Pertanyaan

Untuk 0 < x < 2 π ,nilai 2 sin x + sin 2x cos x + sin 2x cos 3 x + .... = ...

Untuk 0 < x < $\frac{π}{2}$ , nilai 2 sin x + sin 2x cos x + sin 2x $cos^{3}$ x + .... = ...

sin x
cos x
2 sin x
2 sec x
2 csc x

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Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Pembahasan

Dapat dilihat bahwa bentuk tersebut merupakan sebuah deret geometri tak hingga dengan a = 2 sin x, dan

$begin mathsize 14px style straight r equals straight U subscript 2 over straight U subscript 1 equals fraction numerator sin space 2 straight x space cos space straight x over denominator 2 space sin space straight x end fraction straight r equals straight U subscript 2 over straight U subscript 1 equals fraction numerator up diagonal strike 2 space sin space straight x end strike space cos space straight x space cos space straight x over denominator up diagonal strike 2 space sin space straight x end strike end fraction straight r equals cos squared space straight x straight S subscript infinity equals fraction numerator straight a over denominator 1 minus straight r end fraction straight S subscript infinity equals fraction numerator 2 space sin space straight x over denominator 1 minus cos squared space straight x end fraction straight S subscript infinity equals fraction numerator 2 space sin space straight x over denominator sin squared space straight x end fraction straight S subscript infinity equals fraction numerator 2 over denominator sin space straight x end fraction equals 2 space csc space straight x end style$