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Himpunan penyelesaian persamaan trigonometri untuk...

Himpunan penyelesaian persamaan trigonometri cos 2 x degree minus sin x degree equals 0 untuk 0 less or equal than x less or equal than 180 adalah....

  1. {30, 150}

  2. {60, 120}

  3. {30, 60, 150}

  4. {60, 90, 120}

  5. {60, 120, 150}

Jawaban:

Ingat space factorial  cos space 2 straight x equals 1 minus 2 sin squared straight x  cos space 2 straight x equals 2 cos squared straight x minus 1  cos space 2 straight x equals cos squared straight x minus sin squared straight x    cos space 2 straight x minus sin space straight x equals 0  1 minus 2 sin squared straight x minus sin space straight x equals 0  Misalkan space sin space straight x equals straight p  1 minus 2 straight p squared minus straight p equals 0  2 straight p squared plus straight p minus 1 equals 0  open parentheses 2 straight p minus 1 close parentheses open parentheses straight p plus 1 close parentheses equals 0  straight p equals 1 half space atau space straight p equals negative 1  straight p equals 1 half rightwards double arrow sin space straight x equals 1 half rightwards double arrow straight x equals 30 degree comma straight space 150 degree  straight p equals negative 1 rightwards double arrow sin space straight x equals negative 1 rightwards double arrow straight x equals 270 degree space left parenthesis tetapi space tidak space memenuhi space syarat space pada space soal right parenthesis  Sehingga space himpunan space penyelesaian space adalah space open curly brackets 30 degree comma 150 degree close curly brackets

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