4Sinx - 8=0 COSX -1=0

To solve the equations \(4\sin x - 8 = 0\) and \(\cos x - 1 = 0\), we'll handle each equation individually.

Equation 1: \(4\sin x - 8 = 0\)

1. Isolate \(\sin x\): \[ 4 \sin x = 8 \] \[ \sin x = \frac{8}{4} = 2 \]

2. Since the sine function can only take values in the range \([-1, 1]\), there are no solutions for this equation. Thus, there are no \(x\) values that satisfy \(4\sin x - 8 = 0\).

Equation 2: \(\cos x - 1 = 0\)

1. Isolate \(\cos x\): \[ \cos x = 1 \]

2. The cosine function equals 1 at specific angles: \[ x = 2n\pi \quad (n \in \mathbb{Z}) \] This means the solutions occur at all integer multiples of \(2\pi\).

Summary of Solutions

• For \(4\sin x - 8 = 0\): No solutions.
• For \(\cos x - 1 = 0\): \(x = 2n\pi\) where \(n\) is any integer.