How do you prove #cos(x) / (1-sin(x)) = sec(x) + tan(x)#?

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Answer 1 · 2015-12-17T08:43:59

Starting from the right hand side:

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

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

#= ((1+sin(x))(1-sin(x)))/(cos(x)(1-sin(x)))#

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

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

#= cos(x)/(1-sin(x))#