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10. Tentukanlah. c. 2sin2θ+2+2+2cos8θ​​​

Pertanyaan

10. Tentukanlah.

c. square root of 2 space sin squared theta plus square root of 2 plus square root of 2 plus 2 space cos space 8 theta end root end root end root     

Pembahasan:

Ingat kembali rumus cosinus untuk sudut ganda: 

cos space 2 alpha equals cos squared alpha minus sin squared alpha cos space 2 alpha equals 2 times cos squared alpha minus 1  

Oleh karena itu, dapat diperoleh:

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 times sin squared theta plus square root of 2 plus square root of 2 plus 2 times cos space 8 theta end root end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 plus square root of 2 open parentheses 1 plus 1 times cos space 8 theta close parentheses end root end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 plus square root of 2 open parentheses 1 plus cos space 8 theta close parentheses end root end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 plus square root of 2 open parentheses 1 plus cos space 2 open parentheses 4 theta close parentheses close parentheses end root end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 plus square root of 2 open parentheses 1 plus 2 times cos squared 4 theta minus 1 close parentheses end root end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 plus square root of 2 open parentheses 1 minus 1 plus 2 times cos squared 4 theta close parentheses end root end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 plus square root of 2 open parentheses 2 times cos squared 4 theta close parentheses end root end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 plus square root of 4 times cos squared 4 theta end root end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 plus 2 times cos space 4 theta end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 open parentheses 1 plus 1 times cos space 4 theta close parentheses end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 open parentheses 1 plus cos space 4 theta close parentheses end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 open parentheses 1 plus cos space 2 open parentheses 2 theta close parentheses close parentheses end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 open parentheses 1 plus 2 times cos squared 2 theta minus 1 close parentheses end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 open parentheses 1 minus 1 plus 2 times cos squared 2 theta close parentheses end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 2 open parentheses 2 times cos squared 2 theta close parentheses end root end root end cell row blank equals cell square root of 2 times sin squared theta plus square root of 4 times cos squared 2 theta end root end root end cell row blank equals cell square root of 2 times sin squared theta plus 2 times cos space 2 theta end root end cell row blank equals cell square root of 2 times open parentheses sin squared theta plus cos space 2 theta close parentheses end root end cell row blank equals cell square root of 2 times open parentheses sin squared theta plus cos squared theta minus sin squared theta close parentheses end root end cell row blank equals cell square root of 2 times open parentheses cos squared theta close parentheses end root end cell row blank equals cell square root of 2 times cos space theta end cell end table 

Dengan demikian, diperoleh square root of 2 space sin squared theta plus square root of 2 plus square root of 2 plus 2 space cos space 8 theta end root end root end rootadalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 times cos space theta end cell end table.space 

Jawaban terverifikasi

Dijawab oleh:

I. Ridha

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 01 September 2021

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