Question 832149
Verify trigonometric identities
1-sinx/1+sinx=sec^2x-2secxtanx+tan^2x
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{{{(1-sin(x))/(1+sin(x))=sec^2(x)-2sec(x)tan(x)+tan^2(x)}}}
start with left side:
{{{(1-sin(x))/(1+sin(x))}}}
{{{((1-sin(x))/(1+sin(x)))((1-sin(x))/(1-sin(x)))}}}
{{{(1-2sin(x)+sin^2(x))/(1-sin^2(x))}}}
{{{(1-2sin(x)+sin^2(x))/(cos^2(x))}}}
{{{(1/cos^2(x))-(2sin(x)/cos^2(x))+(sin^2(x)/cos^2(x))}}}
{{{(sec^2(x))-(2sin(x)/cos^2(x))+(tan^2(x))}}}
{{{sec^2(x)-2(1/cos(x))(sin(x)/cos(x))+tan^2(x))}}}
{{{sec^2(x)-2sec(x)tan(x)+tan^2(x)}}}
verified: left side=right side