The value of x = 4.71, 0.41, or 5.89 radian value
Specification:
sinxtanx + tanx -2sinx + cosx = 0
tanx = sinx / cosx
sinx (sinx / cosx) + sinx / cosx -2sinx + cosx = Multiply 0
cosx to remove the fraction
sin ^ 2 (x) + sinx -2sinxcosx + cos ^ 2 (x) = 0
sin ^ 2 (x) + cos ^ Replace with 1. 2 (x) = 1
sinx -2sinxcosx + 1 = 0
sinx (1-2cosx) = -1
1-2cosx = -1 / sinx
-2cosx = -1 / sinx -1
2cosx = 1 / sinx + 1
cosx = 1 / 2sinx + 1/2
sqr (1-sin ^ 2 (x)) = 1 / 2sinx + 1/2
Squared on both sides
1-sin ^ 2 (x) = 1 / 4sin ^ 2 (x) + 1 / 2sinx + 1/4
4sin ^ 2 (x) Multiply
4sin ^ 2 (x) -4sin ^ 4 (x) = 1 + 2sinx + sin ^ 2 (X)
4sin ^ 4 (x) -3sin ^ 2 (x) + 2sinx +1 = 0
y = sinx
4y ^ 4 -3y ^ 2 + 2y + 1 = 0
sinx = y = -1 or -0.3478
x = 270, 180-22.61 or -22.61 degrees
x = 270, 157.39 or 337 .39 degrees
or
x = 3pi / 2, 0.13pi or 1.87pi radians
or
x = 4.71, 0.41 Or 5.89 radians
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