How do you prove #\frac { \tan x + \sin x } { \tan x - \sin x } = \frac { \sec x + 1} { \sec x - 1}#?

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Answer 1 · 2017-07-01T08:34:32

See the proof below

We need

#tanx=sinx/cosx#

#1/cosx=secx#

Therefore,

#LHS=(tanx+sinx)/(tanx-sinx)#

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

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

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

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

#=RHS#

#QED#