Question 922184
Prove that the equations are identities.
(secA-tanA)^2=(1-sinA)/(1+sinA)
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use x for A
{{{(secx-tanx)^2=sec^2(x)-2secxtanx+tan^2(x)
=sec^2(x)-2(1/cosx)(sinx/cosx)+(sin^2(x)/cos^2(x))
=1/cos^2(x)-2(1/cosx)(sinx/cosx)+(sin^2(x)/cos^2(x))}}}
{{{1/cos^2(x)-2sinx/cos^2(x)+(sin^2(x)/cos^2(x))
=(1-sinx)^2/(1-sin^2(x))=(1-sinx)^2/(1+sinx)(1-sinx)=(1-sinx)/(1+sinx)}}}
verified: left side=right side