Solve sin2x - 1 = cos2x, where x is between 0 and 360 degrees
My attempt went as follows:
the answer is x = 90, 270, 45, 225
Why is 135 and 315 not correct? Is there a better way of solving this equation?
My attempt went as follows:
Code:
sin2x = cos2x +1
sin[SUP]2[/SUP]2x = (cos2x + 1)[SUP]2[/SUP]
1 - cos[SUP]2[/SUP]2x = cos[SUP]2[/SUP]2x + 2cos2x + 1
0 = 2cos[SUP]2[/SUP]2x + 2cos2x
0 = (2cos2x)(cos2x + 1)
2cos2x = 0 , 2x = 90, 270, 450, 630 , x = 45, 135, 225, 315
cos2x = -1 , 2x = 180, 540 , x = 90, 270
the answer is x = 90, 270, 45, 225
Why is 135 and 315 not correct? Is there a better way of solving this equation?
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