How do you prove #2tan(x)sec(x) = (1/(1-sin(x))) - (1/(1+sin(x)))#?

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Answer 1 · 2018-03-26T08:20:36

Please see explanation.

Here,
#2tanxsecx=1/(1-sinx)-1/(1+sinx)#
We take,

#RHS=1/(1-sinx)-1/(1+sinx)#

#=((1+sinx)-(1-sinx))/((1+sinx)(1-sinx))#

#=(cancel1+sinx-cancel1+sinx)/(1-sin^2x)#

#=(2sinx)/cos^2x#

#=2sinx/cosx1/cosx#, where, #sinx/cosx=tanx and 1/cosx=secx#

#=2tanxsecx#,

#=LHS#