How do you simplify $sinx/(1+cosx)+sinx/(1-cosx)$ ?

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Answer 1 · 2016-11-23T08:46:03

$2cscx$

$sinx/(1+cosx)+sinx/(1-cosx)$

providing $cosx!=+-1$

using the rules of fractions .

$(sinx(1-cosx)+sinx(1+cosx))/((1+cosx)(1-cosx))$

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

$((sinxcancel(-sinxcosx)+sinx+cancel(sinxcosx)))/sin^2x$

$=(2sinx)/sin^2x$

$=(2cancel(sinx))/cancel(sin^2x)^sinx$

$=2/sinx=2cscx$

How do you simplify sinx/(1+cosx)+sinx/(1-cosx)sinx/(1+cosx)+sinx/(1-cosx)?