Question 16
Let $x$ be an angle satisfying
$$\cos x=\sin x+1,\qquad \sin x\lt0.$$
Evaluate
$$\frac{\sin^2 x+\sin x-2}{\sin x-1}\times\frac{\sin^3 x+16\sin^2 x-5\sin x+5}{7\sin^2 x+2\sin x}.$$
Hint: Use $\sin^2 x+\cos^2 x=1$ to determine $\sin x$. You do not need to find $x$.
$$\cos x=\sin x+1,\qquad \sin x\lt0.$$
Evaluate
$$\frac{\sin^2 x+\sin x-2}{\sin x-1}\times\frac{\sin^3 x+16\sin^2 x-5\sin x+5}{7\sin^2 x+2\sin x}.$$
Hint: Use $\sin^2 x+\cos^2 x=1$ to determine $\sin x$. You do not need to find $x$.