Solve the following equation for 0°≤x≤360°.
(Give your answers correct to 1 decimal place if necessary.)
sin^2 x-2sinxcosx-cos^2 x=0
F.4 Maths
2010-03-05 7:29 am
回答 (2)
2010-03-05 7:52 am
✔ 最佳答案
sin^2 x-2sinxcosx-cos^2 x=0cos x not = 0 ,
(cos^2 x)(sin^2 x / cos^2 x - 2sinx/cosx - 1) = 0
(cos^2 x)(tan^2 x - 2tanx - 1) = 0
cos^2 x = 0 or tan^2 x - 2tanx - 1 = 0
cos x = 0(rejected) or tan x = [2 +/- √ (2^2 - 4(1)(-1))]/2
tan x = 1 + √ 2 or 1 - √ 2
x = 67.5° , (180+67.5)° or 157.5° , (180+157.5)°
x = 67.5° , 247.5° or 157.5° , 337.5°
2010-03-05 5:23 pm
cos^2 x - sin^2 x = - 2 sin x cos x
cos 2x = - sin 2x
tan 2x = -1
2x = 135, 315, 495 or 675
x = 67.5, 157.5, 247.5 or 337.5
cos 2x = - sin 2x
tan 2x = -1
2x = 135, 315, 495 or 675
x = 67.5, 157.5, 247.5 or 337.5
收錄日期: 2021-04-21 22:09:54
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