Dr. Merritt Quitzon
Feb 15, 2025
cos 4x – sin2x = 0 ? Trigonometry?
I have the equation cos(4x) – sin(2x) = 0 that I need help solving. Please note that it is not cos^4(x) or sin^2(x). I am looking for solutions within the domain of 0 to 2π or 0 to 360 degrees. Could you please provide a step-by-step explanation of how to obtain the solutions: 15°, 75°, and -45°? Thank you!
2 Answers
1- 2(sin2x)^2 – sin2x = 0—>2(sin2x)^2 + sin2x – 1 = 0
(sin2x +1)(2sin2x – 1) = 0
sin2x + 1 = 0—>sin2x = -1 —> 2x = 270, 630 —>x = 135, 315
2sin2x – 1 = 0 —> sin2x = 1/2 —>2x = 30, 150, 390, 510
—> x = 15, 75, 195, 255
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