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Another contributor says:
Yes, x=0 is a solution, but there are a lot more.
sin(2x) = sin(x) whenever
x = (N pi) radians
or
x = (2N-1) pi / 3 radians.
1 radian = 57.3 degrees (rounded)
Make ' N ' any whole number you want.
The first cycle of angles are:
X = pi/3, pi, 5 pi/3, 2 pi radians
or 60, 180, 300, 360 degrees.
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to simplify Cosx=Sinx Tanx you should remember your fundamental and pythagorean identities.. Cosx + Sinx Tanx Cosx + Sinx (Sinx/Cosx) <---------- From Tanx= Sinx/Cosx Cosx + Sin2x/ Cos x <------------- do the LCD Cosx (Cosx/Cosx) + Sin2x/Cosx (Cos2x+Sin2x)/Cosx 1/Cosx <--------- From Sin2x + Cos2x =1 or Secx <-------- answer Comment if you have questions...:))
2sinxsinx=1 (sinx)(sinx)=1/2 sinx=1/4=o.25 since, roughly, for small x values, sin x = x then x=0.25 Otherwise, to be more accurate, we proceed as follows: sinx=0.25 (as given before) then x=arc sin 0.25=0.2526803
cosx + sinx = 0 when sinx = -cosx. By dividing both sides by cosx you get: sinx/cosx = -1 tanx = -1 The values where tanx = -1 are 3pi/4, 7pi/4, etc. Those are equivalent to 135 degrees, 315 degrees, etc.
sqrt(2)*cos(x + pi/4) [with x in radians], or sqrt(2)*cos(x + 90°) [with x in degrees]
2sinxcosx-cosx=0 Factored : cosx(2sinx-1)=0 2 solutions: cosx=0 or sinx=.5 For cosx=0, x=90 or 270 degrees For sinx=.5, x=30 degrees x = {30, 90, 270}