b) \( (1-\sin x)^{2}+\cos ^{2} x=2(1-\sin x) \)

Resolve the equation \( (1-\sin x)^{2}+\cos ^{2} x=2(1-\sin x) \). Solve the equation by following steps: - step0: Solve for \(x\): \(\left(1-\sin\left(x\right)\right)^{2}+\cos^{2}\left(x\right)=2\left(1-\sin\left(x\right)\right)\) - step1: Multiply the terms: \(\left(1-\sin\left(x\right)\right)^{2}+\cos^{2}\left(x\right)=2-2\sin\left(x\right)\) - step2: Move the expression to the left side: \(\left(1-\sin\left(x\right)\right)^{2}+\cos^{2}\left(x\right)-\left(2-2\sin\left(x\right)\right)=0\) - step3: Remove the parentheses: \(\left(1-\sin\left(x\right)\right)^{2}+\cos^{2}\left(x\right)-2+2\sin\left(x\right)=0\) - step4: Calculate: \(-1+\sin^{2}\left(x\right)+\cos^{2}\left(x\right)=0\) - step5: Rewrite the expression: \(0=0\) - step6: The statement is true: \(x \in \mathbb{R}\) La solution de l'équation \( (1-\sin x)^{2}+\cos ^{2} x=2(1-\sin x) \) est \( x \in \mathbb{R} \), ce qui signifie que la solution est vraie pour tous les nombres réels \( x \).