Perhatikan bahwa
Ingat bahwa
![begin mathsize 14px style A cos invisible function application x plus B sin invisible function application x equals k cos invisible function application open parentheses x minus alpha close parentheses end style](data:image/png;base64,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)
dengan syarat
dan ![begin mathsize 14px style alpha equals tan to the power of negative 1 end exponent invisible function application open parentheses B over A close parentheses end style](data:image/png;base64,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)
Maka, dari
dengan
dan
, didapat
dan
Perhatikan bahwa A berhubungan dengan cos x dan B berhubungan dengan sin x. Kemudian A bernilai positif dan B bernilai positif.
Kuadran dengan cosinus sudut yang bernilai positif dan sinus sudut yang bernilai positif terdapat pada kuadran I. Sehingga α berada pada kuadran I.
Karena
, maka
.
Sehingga
![begin mathsize 14px style 3 cos invisible function application 2 x plus square root of 3 sin invisible function application 2 x equals 2 square root of 3 cos invisible function application open parentheses 2 x minus 30 degree close parentheses end style](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQoAAAAQCAYAAADu8TGAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAABB5JREFUeNrtW0FIFFEYHhZZIiIIkwyJjUXEg0ggoSJhxxCJqEOBdQhDIiK6mURQRBQda/ES0UFKiCVCpAIPEtIhEhHqIEaJSIR4KGKJWBa2/+E3Mbx9b+afcd/s5L4PPtyZebvz/m/++fb/36yOY8HFLuIcsRyBFlZbizrBGeKslcFqa2Hhh9fEs1aGutV2jHi9Tq7HGGgREs3EH8S9Voq61PY4cXKb6n+JWCD+wmsXTxF3hRDzxCLxN/EN8XCMkx1Ej1rE33H0rdXEVvrZi5pEqZZu5YRqFsdcTGu7VTQQvxAbE6Y9V58+4gLGLRKPSMeFQRwgZvHahYh3mZj2Dn5J7CamIMwV4mqMQU8T+3F+gWFiPkFG8QHJIaOWusWhWRxzSaK2XohYHiRQe44+4uZfInZhuws3f9YzRlQTrcSMZBQO4h4OctGNGpZDKbhkEoziIErjBua3z8Y20sz0XP4HbfMaI0ua9ip9coob/Tz2uxgh/oRJjCgqxbwu4E7iY404wnme44MvS8eGiGvgkOK9J3GsxLhpMyj3VC7a69neQ5wh7jdoFLeJDxmJ4qdbUPyq7TbEJhJwhTgQk2bVeBypm4spbU3m5jqjrTCRr2FMWaePmFOTtK8xRGW2U2XObiKsIXAZov+ZIrZAuJzUB00Qd6CnmdD0QhnmBMV5Tij2t6AvS+E8eSRIlITnJv1H4tEAA/LTjRO/yig+QYMUSsxvMWhWLejmYkpbk7lZSki+RtFHN/diiGtZ1LlTLwLqlo7N+wQ5J7nkPuJbaYzolUZxwXQQF1m52urBKPiEeKiKrcdNjOn07OshfmaUxn66ceJXGUUrc/4mNQsL3VxMa2syN0s1ytcwFYVOH93c/2zVKFw0YdGD+4YiY1878R3xO/GYYry4gJOMb7ssBOg3sEbxjPjVsy3K4rshzqHSjRN/mTHXckyaRa3CguZiUluTuSn27a5BvoaFSp9lRevRxGwLXSNcD3KpguKkWc34WQjn59ouBiC+I/VuL/A3SAxxQU8TbxkwCgdrAlc9SdIe0t0LAWNU8Ucxijg044I7F1PamsxN1WJmkrT30yeHxUt5MXOc+ZkVi5nTnrJFuOd9p/KRkBDxFco40W/dU/SBaZRvqj7QRYfiYkxhf5C7zXjGPXLCPVfnGsUFJPQpZ/PRnR84unHij2IUcWgWZk2io4bamsxN1ePRJGjP0cd9POq2PN2oJrLMc1QYzSD6vBIWze5oesc2TFCIeU46NoT3rsBBdSXtqqb09itz0zhvn2efWL19H7DmERVLOP81huNydOPEH9YokqRZmDbFhLYmczONiqUxYdpz9RGmuIh2a8HHJFWt1ZIj/eDKojLpxIVvtlJYbZ3t/RNuHYIWaS2AHiuB1daDevpHqRvO5pOaf/gLUGvZLeyrShoAAAGgdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdHlsZSBtYXRoc2l6ZT0iMTRweCI+PG1uPjM8L21uPjxtaT5jb3M8L21pPjxtbz4mI3gyMDYxOzwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1zcXJ0Pjxtbj4zPC9tbj48L21zcXJ0PjxtaT5zaW48L21pPjxtbz4mI3gyMDYxOzwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bW8+PTwvbW8+PG1uPjI8L21uPjxtc3FydD48bW4+MzwvbW4+PC9tc3FydD48bWk+Y29zPC9taT48bW8+JiN4MjA2MTs8L21vPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4yPC9tbj48bWk+eDwvbWk+PG1vPi08L21vPjxtbj4zMDwvbW4+PG1vPiYjeEIwOzwvbW8+PC9tcm93PjwvbWZlbmNlZD48L21zdHlsZT48L21hdGg+lqtY5wAAAABJRU5ErkJggg==)
Maka
Ingat bahwa pada persamaan
, maka
atau
.
Sehingga dari persamaan
, didapat
Atau
Perhatikan bahwa pada soal diketahui interval
, yang berarti
.
Untuk
,
Jika k = 0, maka x = 45° + 0⋅180° = 45°.
Jika k = 1, maka x = 45° + 1⋅180° = 225° (tidak memenuhi).
Jika k =
1, maka x = 45° + (
1)⋅180° =
135°.
Jika k =
2, maka x = 45° + (
2)⋅180° =
315° (tidak memenuhi).
Untuk
,
Jika k = 0, maka x =
15° + 0⋅180° =
15°.
Jika k = 1, maka x =
15° + 1⋅180° = 165°.
Jika k = 2, maka x =
15° + 2⋅180° = 345° (tidak memenuhi).
Jika k =
1, maka x =
15° + (
1)⋅180° =
195° (tidak memenuhi).
Sehingga himpunan penyelesaian dari persamaan
pada interval
adalah
.
Karena interval pada soal adalah dalam radian, maka himpunan penyelesaian tersebut dapat ditulis sebagai
.
Jadi, jawaban yang tepat adalah A.