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標題:

math question 23

發問:

find all real number in the interval (0,360)that satisfy the equation. use degree measure 2sec^2xtanx=4tanx the solution set is ? round to the nearest tenth as needed. do not include the degree symbol in your answer. use a comma to separate answers as needed.

最佳解答:

find all real number in the interval (0,360)that satisfy the equation. use degree measure 2sec^2xtanx=4tanx 2(tan^2x+1)tanx=4tanx 2tan^3x+2tanx-4tanx=0 2(tan^2x-1)tanx=0 (tan^2x-1)=0 or tanx=0 tan^2x=1 or tanx=0 tanx=1 or tanx=-1 or tanx=0 (x=45 or 225) or (x=135or 315) or (x=0 or 360) so, x={0,45,135,225,315,360}

其他解答:

2sec^2x tanx = 4tanx => 2sec^2x tanx - 4tanx = 0 => tanx(sec^2x - 2) = 0 => tanx (sec x - sqrt(2)) (sec x + sqrt(2)) = 0 where sqrt(2) means square root 2 => tan x = 0 or sec x - sqrt 2 = 0 or sec x + sqrt 2 = 0 With 0 < x < 360, For tan x = 0, x = 180 For sec x - sqrt 2 = 0 or cos x = sqrt(2)/2, x = 45, 225 For sec x + sqrt 2 = 0 or cos x = -sqrt(2)/2, x = 135, 315 Therefore, the overall solution is x = 45, 135, 180, 225 or 315.

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