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

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Answer 1 · 2015-07-04T05:19:18

It can be proved by #sec^2x-tan^2x=1#

#sec^2x-tan^2x=1#

#(secx+tanx)(secx-tanx)=1#[since#a^2-b^2=(a+b)(a-b)]#

#secx+tanx=1/(secx-tanx)##" " color(red)((1))#

#secx-tanx=1/(secx+tanx)##" " color(red)((2))#

#LHS= (1/(secx−tanx)−1/(secx+tanx))#

#" " color(red)((1))#&#color(red)((2))# substitute in the above equation

#LHS=(secx+tanx)-(secx-tanx)#

#LHS=secx+tanx-secx+tanx#

#LHS=2tanx#

#LHS=RHS#

Hence proved