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