How do you simplify #cosx/(1+sinx) + (1+sinx)/cosx#?

1 Answer
George C.
May 23, 2018

#(cos x)/(1 + sin x) + (1 + sin x)/(cos x) = 2 sec x#

Explanation:

#(cos x)/(1 + sin x) + (1 + sin x)/(cos x) = (cos^2x + (1 + sin x)^2)/((1+sin x)cos x)#

#color(white)((cos x)/(1 + sin x) + (1 + sin x)/(cos x)) = (cos^2x + sin^2x + 1 + 2sinx)/((1+sin x)cos x)#

#color(white)((cos x)/(1 + sin x) + (1 + sin x)/(cos x)) = (2 + 2sinx)/((1+sin x)cos x)#

#color(white)((cos x)/(1 + sin x) + (1 + sin x)/(cos x)) = (2color(red)(cancel(color(black)((1 + sinx)))))/(color(red)(cancel(color(black)((1+sin x))))cos x)#

#color(white)((cos x)/(1 + sin x) + (1 + sin x)/(cos x)) = 2/cos x#

#color(white)((cos x)/(1 + sin x) + (1 + sin x)/(cos x)) = 2sec x#

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