How do you verify $(1-sin)/(1+sin) = (sec-tan)^2$ ?

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Answer 1 · 2016-10-12T17:16:45

see below

$(1-sinx)/(1+sinx) = (secx-tanx)^2$

Left Side : $=(1-sinx)/(1+sinx)$

$=(1-sinx)/(1+sinx) * (1-sinx)/(1-sinx)$

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

$=(1-2sinx+sin^2x)/cos^2x$

$=1/cos^2x-(2sinx)/cos^2x+sin^2x/cos^2x$

$=1/cos^2x-2 * 1/cosx sinx/cosx+sin^2x/cos^2x$

$=sec^2x-2secxtanx+tan^2x$

$=(secx-tanx)(secx-tanx)$

$=(secx-tanx)^2$

$:.=$ Right Side

How do you verify (1-sin)/(1+sin) = (sec-tan)^2(1-sin)/(1+sin) = (sec-tan)^2?