Simplify the following

Question

cos theta + 1

----------------

1 + sec theta

Answer 1

cos theta +1/1+sec theta can be simplified by rewriting secant theta as 1/cos theta on the bottom.

We get cos theta+1 in the numerator divided by (1+ 1/cos theta) on the bottom. I am going to work with the bottom only and add 1 to 1/cos theta. To this end, I rewrite 1 as cos theta/cos theta. Adding it to 1/cos theta gives me (cos theta +1)/cos theta as the new denominator.

 

Thus my new fraction is cos theta +1/ ((cos theta+1)/cos theta)). Dividing is the same as multiplying by the reciprocal therefore, this fraction is the same as (cos theta+1) *cos theta/(cos theta+1). Since both the numerator and denominator have the same factor aka ( cos theta +1), i cross them out from both, and I am left with only cos theta. That is the answer