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

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Answer 1 · 2018-03-17T05:27:33

Please refer to the Explanation.

We have, #cosx/(1-sinx)#,

#=cosx/(1-sinx)xx1#,

#=cosx/(1-sinx)xx(1+sinx)/(1+sinx)#,

#={cosx(1+sinx)}/{1-sin^2x)#,

#={cosx(1+sinx)}/cos^2x#,

#=(1+sinx)/cosx#,

#=1/cosx+sinx/cosx#,

#=secx+tanx#, as desired!

Enjoy Maths.!