How do you prove $(1-cosx)(1+secx)=sinxtanx$ ?

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Answer 1 · 2015-04-15T04:31:22

$f(x) = (1 - cos x)(1 + 1/cos x) = (1 - cos x) (cos x + 1)/cos x = (1 - cos^2 x)/cos x = sin^2 x/cos x = sin x*(sin x/cos x) = sin x*tan x$

Reminder:
$(1 - cos x)(1 + cos x) = (1 - cos ^2 x) = sin^2 x$

How do you prove (1-cosx)(1+secx)=sinxtanx(1-cosx)(1+secx)=sinxtanx?