To solve this trigonometric equation, we will use the properties of sin and cos functions.
Given: sin(4π - x) - cos(3π/2 + x) + 1 = 0
Recall the trigonometric identities:a) sin(π/2 + θ) = cos(θ)b) cos(π + θ) = -cos(θ)c) sin(2π - θ) = sin(θ)
Substitute sin(4π - x) using identity c:sin(4π - x) = sin(x)
Substitute cos(3π/2 + x) using identity a:cos(3π/2 + x) = sin(x)
Substituting these values into the equation:sin(x) - sin(x) + 1 = 00 + 1 = 01 = 0
Since the equation produced a contradiction, the original trigonometric equation sin(4π - x) - cos(3π/2 + x) + 1 = 0 has no solutions.
To solve this trigonometric equation, we will use the properties of sin and cos functions.
Given: sin(4π - x) - cos(3π/2 + x) + 1 = 0
Recall the trigonometric identities:
a) sin(π/2 + θ) = cos(θ)
b) cos(π + θ) = -cos(θ)
c) sin(2π - θ) = sin(θ)
Substitute sin(4π - x) using identity c:
sin(4π - x) = sin(x)
Substitute cos(3π/2 + x) using identity a:
cos(3π/2 + x) = sin(x)
Substituting these values into the equation:
sin(x) - sin(x) + 1 = 0
0 + 1 = 0
1 = 0
Since the equation produced a contradiction, the original trigonometric equation sin(4π - x) - cos(3π/2 + x) + 1 = 0 has no solutions.