How do you simplify $(1+cos y)/(1+sec y)$ ?

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Answer 1 · 2015-08-05T22:00:47

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

$secy=1/cosy$ , therefore we have:

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

Answer 2 · 2015-08-06T01:23:26

Since $secy = 1/cosy$ , you can rewrite this as:

$(1+cosy)/(1+(1/cosy))$

Thus, multiply through by $((cosy)/(cosy))$ :

$= (cosy+cos^2y)/(cosy+1)$

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

$= color(blue)(cosy)$

How do you simplify (1+cos y)/(1+sec y)(1+cos y)/(1+sec y)?