Questions: Simplify and write the trigonometric expression in terms of sine and cosine: (1+cos y)/(1+sec y)=□

Solution Steps

$$\sec y = \frac{1}{\cos y}$$

$$\frac{1 + \cos y}{1 + \sec y} = \frac{1 + \cos y}{1 + \frac{1}{\cos y}}$$

$$1 + \frac{1}{\cos y} = \frac{\cos y + 1}{\cos y}$$

$$\frac{1 + \cos y}{\frac{\cos y + 1}{\cos y}} = (1 + \cos y) \cdot \frac{\cos y}{\cos y + 1}$$

$$(1 + \cos y) \cdot \frac{\cos y}{\cos y + 1} = \cos y$$

The expression simplifies to $\cos y$.

Final Answer