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Apabila , maka nilai dari  adalah ...

Apabila tan space theta equals fraction numerator 1 over denominator square root of 7 end fraction, maka nilai dari open parentheses fraction numerator cos e c squared theta minus s e c squared theta over denominator cos e c squared theta plus s e c squared theta end fraction close parentheses adalah ...

  1. 1 over 12 

  2. 3 over 7 

  3. 3 over 4 

  4. 5 over 7 

  5. 4 over 3 

Jawaban:

Diketahui tan space theta equals fraction numerator 1 over denominator square root of 7 end fraction.

d e equals 1 s a equals square root of 7

table attributes columnalign right center left columnspacing 0px end attributes row cell m i end cell equals cell square root of d e squared plus s a squared end root end cell row blank equals cell square root of 1 squared plus open parentheses square root of 7 close parentheses squared end root end cell row blank equals cell square root of 1 plus 7 end root end cell row blank equals cell square root of 8 end cell row blank equals cell 2 square root of 2 end cell end table 

Nilai dari open parentheses fraction numerator cos e c squared theta minus s e c squared theta over denominator cos e c squared theta plus s e c squared theta end fraction close parentheses:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator cos e c squared theta minus s e c squared theta over denominator cos e c squared theta plus s e c squared theta end fraction close parentheses end cell equals cell open parentheses fraction numerator open parentheses begin display style fraction numerator m i over denominator d e end fraction end style close parentheses squared minus open parentheses begin display style fraction numerator m i over denominator s a end fraction end style close parentheses squared over denominator open parentheses begin display style fraction numerator m i over denominator d e end fraction end style close parentheses squared plus open parentheses begin display style fraction numerator m i over denominator s a end fraction end style close parentheses squared end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator open parentheses begin display style fraction numerator 2 square root of 2 over denominator 1 end fraction end style close parentheses squared minus open parentheses begin display style fraction numerator 2 square root of 2 over denominator square root of 7 end fraction end style close parentheses squared over denominator open parentheses begin display style fraction numerator 2 square root of 2 over denominator 1 end fraction end style close parentheses squared plus open parentheses begin display style fraction numerator 2 square root of 2 over denominator square root of 7 end fraction end style close parentheses squared end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 4 times 2 minus begin display style fraction numerator 4 times 2 over denominator 7 end fraction end style over denominator 4 times 2 plus begin display style fraction numerator 4 times 2 over denominator 7 end fraction end style end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 8 minus begin display style 8 over 7 end style over denominator 8 plus begin display style 8 over 7 end style end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator begin display style fraction numerator 56 minus 8 over denominator 7 end fraction end style over denominator begin display style fraction numerator 56 plus 8 over denominator 7 end fraction end style end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator begin display style 48 over 7 end style over denominator begin display style 64 over 7 end style end fraction close parentheses end cell row blank equals cell 48 over 64 end cell row blank equals cell 3 over 4 end cell end table 

Sehingga, nilai dari open parentheses fraction numerator cos e c squared theta minus s e c squared theta over denominator cos e c squared theta plus s e c squared theta end fraction close parentheses adalah 3 over 4.

Jadi, jawaban yang tepat adalah C.

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