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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.
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}
(1 + tanx)/sinxMultiply by sinx/sinxsinx + tanxsinxDivide by sin2x (1/sin2x) = cscxcscx + tan(x)csc(x)tanx = sinx/cosx and cscx = 1/sinxcscx + (sinx/cosx)(1/sinx)sinx cancels outcscx + 1/cosx1/cosx = secxcscx + secx
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...:))
There is not a "reverse" - whatever that may mean. The solution is x = (-0.6662 + 2k*pi) radians where k is an integer.
The solitions are in degrees. You may convert them to degrees should you wish. x= 0,90,120,180,240,270,360
(1 - csc2x)/(sinx*cotx) = -cot2x/sinxcotx = -cotx/sinx = -(cosx/sinx)/sinx = -cosx/sin2x = -cosx/(1-cos2x) = cosx/(cos2x - 1)
d/dx (sin x + sin 2x) = cos x + 2cos 2x
d/dx cscx = d/dx 1/sinx = d/dx (sinx)-1= -(sinx)-2 cosx = -cosx/sin2x = -1/sinx.cosx/sinx = -cscx cotx I suggest you copy this out onto paper so it is more clear. The / signs make it harder to see what is happening compared to horizontal divide lines.
you need this identities to solve the problem..that is something you have to memorized sec x= 1/cosx 1-cos2x= sin2x tanx= sin x/cosx also, sin 2x= (sinx)(sinx) sec x - cosx= sin x tanx (1/cosx)-cosx= sin x tanx .. 1-cos2x / cosx=sin x tanx sin2x/ cosx= sin x tanx (sin x/cox)( sin x)= sin x tanx tanx sinx= sin x tanx
4 sin2x = 1. Then, (2sinx)2 = 1, 2sinx = ±1, and sinx = ±½. Whence, x = 90° or 270°; or, in radians, x = π/2 or 3π/2.
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
f(x) = 1/x except where x = 0.
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