How do you simplify $1/(cscx - cotx) + 1/(cscx + cotx)$ ?

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Answer 1 · 2015-08-30T01:10:34

$2cscx$

Rewrite in terms of $sinx$ and $cosx$

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

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

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

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

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

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

$(2sinx)/sin^2x$

$2/sinx$

$2cscx$

How do you simplify 1/(cscx - cotx) + 1/(cscx + cotx) 1/(cscx - cotx) + 1/(cscx + cotx)?