How do you prove $1/(secx-tanx) - 1/(secx+tanx)=2tanx$ ?

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Answer 1 · 2016-05-11T18:13:50

see below

Use Property: $sec^2x=1+tan^2x$

Left Side: $=1/(secx-tanx) -1/(secx+tanx)$

$=(secx+tanx-(secx-tanx))/((secx-tanx)(secx+tanx))$

$=(secx+tanx-secx+tanx)/(sec^2x-tan^2x)$

$=(2tanx)/1$

$=2tanx$

$=$ Right Side

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