How do you simplify $\frac{1 + cos y}{1 + sec y}$ $(1+cos y)/(1+sec y)$ ?

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How do you simplify $\frac{1 + cos y}{1 + sec y}$ $(1+cos y)/(1+sec y)$ ?

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Answer 1 · 2015-08-05T22:00:47

$\frac{1 + cos y}{1 + sec y} = cos y$ $(1+cosy)/(1+secy)=cosy$

Explanation:

$sec y = \frac{1}{cos y}$ $secy=1/cosy$ , therefore we have:

$\frac{1 + cos y}{1 + sec y} = (\frac{cos y}{cos y}) (\frac{1 + cos y}{1 + \frac{1}{cos y}}) =$ $(1+cosy)/(1+secy)=(cosy/cosy)((1+cosy)/(1+1/cosy))=$
$cos y (\frac{1 + cos y}{1 + cos y}) = cos y$ $cosy((1+cosy)/(1+cosy))=cosy$

Answer 2 · 2015-08-06T01:23:26

Since $sec y = \frac{1}{cos y}$ $secy = 1/cosy$ , you can rewrite this as:

$\frac{1 + cos y}{1 + (\frac{1}{cos y})}$ $(1+cosy)/(1+(1/cosy))$

Thus, multiply through by $(\frac{cos y}{cos y})$ $((cosy)/(cosy))$ :

$= \frac{cos y + {cos}^{2} y}{cos y + 1}$ $= (cosy+cos^2y)/(cosy+1)$

$= cosy(cancel((1+cosy)/(cosy+1)))$

$= color(blue)(cosy)$

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How do you simplify $\frac{1 + cos y}{1 + sec y}$ $(1+cos y)/(1+sec y)$ ?

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