How do you prove #4tanxsecx=((1+sinx)/(1-sinx))-((1-sinx)/(1+sinx))#?

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Answer 1 · 2016-11-05T16:34:25

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

#=(2-(1-sinx))/(1-sinx)-(2-(1+sinx))/(1+sinx)#

#=(2/(1-sinx)-(1-sinx)/(1-sinx))-(2/(1+sinx)-(1+sinx)/(1+sinx))#

#=(2/(1-sinx)-cancel1-2/(1+sinx)+cancel1)#

#=2(1/(1-sinx)-1/(1+sinx))#

#=2((1+sinx-1+sinx)/((1-sinx)(1+sinx)))#

#=(4sinx)/(1-sin^2x)#

#=(4sinx)/cos^2x#

#=(4sinx)/cosx xx1/cosx#

#=4tanxsecx=LHS#

Proved