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Himpunan semua bilangan real x pada selang yang me...

Himpunan semua bilangan real x pada selang left square bracket straight pi comma space 2 straight pi right square bracket yang memenuhi 2 cos open parentheses straight pi over 2 minus x close parentheses cos x greater or equal than 1 minus cos 2 x berbentuk [a,b]. Nilai a+b adalah....

  1. fraction numerator 9 straight pi over denominator 4 end fraction

  2. 3 straight pi

  3. fraction numerator 13 straight pi over denominator 4 end fraction

  4. fraction numerator 14 straight pi over denominator 4 end fraction

  5. fraction numerator 15 straight pi over denominator 4 end fraction

Jawaban:

2 cos invisible function application open parentheses straight pi over 2 minus straight x close parentheses cos invisible function application straight x greater or equal than 1 minus cos invisible function application 2 straight x  2 sin invisible function application xcos invisible function application straight x greater or equal than 1 minus left parenthesis 1 minus 2 sin squared invisible function application straight x right parenthesis  2 sin invisible function application xcos invisible function application straight x greater or equal than 2 sin squared invisible function application straight x  2 sin invisible function application xcos invisible function application straight x minus 2 sin squared invisible function application straight x greater or equal than 0  sin invisible function application xcos invisible function application straight x minus sin squared invisible function application straight x greater or equal than 0  sin invisible function application straight x left parenthesis cos invisible function application straight x minus sin invisible function application straight x right parenthesis greater or equal than 0  Didapat space pembuat space nol comma space yaitu  box enclose sin invisible function application straight x equals 0 end enclose space atau space box enclose sin space straight x equals cos space straight x end enclose    Untuk space sin space straight x equals 0 rightwards double arrow box enclose straight x equals straight pi comma 2 straight pi end enclose  Untuk space sin space straight x equals cos space straight x rightwards double arrow tan space straight x equals 1 rightwards double arrow box enclose straight x equals 5 over 4 straight pi end enclose

Maka space didapat space straight pi less or equal than straight x less or equal than 5 over 4 straight pi space atau space open square brackets straight pi comma 5 over 4 straight pi close square brackets.    Sehingga space straight a plus straight b equals straight pi plus 5 over 4 straight pi equals box enclose 9 over 4 straight pi end enclose

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