Question #879e2

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Answer 1 · 2016-11-15T01:47:23

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

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

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

$=(1-cosx)/sinx+(sinx(1+cosx))/sin^2x$

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

$=1/sinx-cosx/sinx+1/sinx+cosx/sinx$

$=2/sinx=RHS$

Proved