solve the equation for all exact solutions where appropriate\nround approximate answers in degrees to the…

Explanation:

Step1: Simplify the equation

Use the identity (\sec\theta=\frac{1}{\cos\theta}). The given equation (\sin\theta\sec\theta - \sin\theta = 0) becomes (\sin\theta\frac{1}{\cos\theta}-\sin\theta = 0). Factor out (\sin\theta): (\sin\theta(\frac{1}{\cos\theta}- 1)=0).

Step2: Set each factor equal to zero

Case 1: (\sin\theta = 0). The general solution for (\sin\theta=0) is (\theta = 180^{\circ}n), where (n\in\mathbb{Z}) (using the unit - circle, (\sin\theta = y) - coordinate on the unit circle, and (y = 0) when (\theta=0^{\circ},180^{\circ},360^{\circ},\cdots)). Case 2: (\frac{1}{\cos\theta}-1 = 0). (\frac{1}{\cos\theta}=1), then (\cos\theta = 1). The general solution for (\cos\theta = 1) is also (\theta = 360^{\circ}n=180^{\circ}(2n)) ((n\in\mathbb{Z})).

Answer:

D. ({180^{\circ}n,\text{ where }n\text{ is any integer}})