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Untuk 0 < x < π , maka semua nilai x yang memenuhi pertidaksamaan cos x 2 − sin x ​ < sin x cos x ​ adalah....

Untuk , maka semua nilai x yang memenuhi pertidaksamaan  adalah....

  1. 0 less than straight x less than straight pi over 6 atau straight pi over 2 less than straight x less than fraction numerator 5 straight pi over denominator 6 end fraction

  2. straight pi over 6 less than straight x less than straight pi over 2 atau fraction numerator 5 straight pi over denominator 6 end fraction less than straight x less than straight pi

  3. 0 less than straight x less than straight pi over 2 atau straight pi over 2 less than straight x less than fraction numerator 5 straight pi over denominator 6 end fraction

  4. 0 less than straight x less than straight pi over 3 atau straight pi over 2 less than straight x less than fraction numerator 2 straight pi over denominator 3 end fraction

  5. straight pi over 6 less than straight x less than straight pi over 3 atau fraction numerator 5 straight pi over denominator 6 end fraction less than straight x less than straight pi

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Pembahasan

* maka atau ** maka dan maka Penyelesaiannya adalah atau

fraction numerator 2 minus sin space straight x over denominator cos space straight x end fraction less than fraction numerator cos space straight x over denominator sin space straight x end fraction rightwards double arrow fraction numerator 2 minus sin space straight x over denominator cos space straight x end fraction minus fraction numerator cos space straight x over denominator sin space straight x end fraction less than 0 rightwards double arrow fraction numerator 2 space sin space straight x space minus space sin space straight x over denominator sin space straight x space cos space straight x end fraction less than 0 rightwards double arrow fraction numerator 2 space sin space straight x space 1 over denominator sin space straight x space cos space straight x end fraction less than 0

2 space sin space straight x equals 1 maka straight x equals 30 degree atau straight x equals 150 degree

** cos space straight x equals 1 maka straight x equals 90 degreedan sin space straight x equals 0 maka straight x equals 0 degree

Penyelesaiannya adalah 0 less than straight x less than straight pi over 6 atau straight pi over 2 less than straight x less than fraction numerator 5 straight pi over denominator 6 end fraction

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