How do you prove #cosX / (secX - tanX) = 1 + sinX#?

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Answer 1 · 2018-03-11T07:50:54

As below.

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

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L H S # = cos x / ((1/cos x) - (sin x / cos x)# as #color(blue)(sec x = 1/cos x, tan x = sin x / cos x#

#=> cos x / ((1 - sin x) / cos x)# as #color(green)(cos x # is the L C M of Denominator.

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

#=> = (1 - sin^2 x) / (1 - sin x)# as #color(blue)(cos^2x = 1 - sin^2x#

#=> ((1+ sin x) *color(red)(cancel (1 - sin x))) /color(red)(cancel (1 - sin x))#

#=> 1 + sin x#

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