Drag and drop the correct answer into the space(s) provided, Determine all solutions of the equation \( 8 \sin x+7=10 \sin x+1 \), \[ x=\square, n \in \mathbb{Z} \] \( \frac{\pi}{2}+2 n \pi \) \( \frac{\pi}{2}+n \pi \) \( \pi+2 n \pi \) \( \pi+n \pi \)

Solve the equation \( 8 \sin x+7=10 \sin x+1 \). Solve the equation by following steps: - step0: Solve for \(x\): \(8\sin\left(x\right)+7=10\sin\left(x\right)+1\) - step1: Move the expression to the left side: \(8\sin\left(x\right)+7-\left(10\sin\left(x\right)+1\right)=0\) - step2: Calculate: \(-2\sin\left(x\right)+6=0\) - step3: Move the constant to the right side: \(-2\sin\left(x\right)=0-6\) - step4: Remove 0: \(-2\sin\left(x\right)=-6\) - step5: Change the signs: \(2\sin\left(x\right)=6\) - step6: Divide both sides: \(\frac{2\sin\left(x\right)}{2}=\frac{6}{2}\) - step7: Divide the numbers: \(\sin\left(x\right)=3\) - step8: Rearrange the terms: \(x \notin \mathbb{R}\) The equation \(8 \sin x + 7 = 10 \sin x + 1\) does not have any real solutions. Therefore, there are no solutions for \(x\) in the form of \(\frac{\pi}{2} + 2n\pi\), \(\frac{\pi}{2} + n\pi\), \(\pi + 2n\pi\), or \(\pi + n\pi\).