How do you verify $sinx/(1-cosx) + (1-cosx)/sinx = 2cscx$ ?

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Answer 1 · 2018-03-06T20:51:10

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$LHS: sin x/(1-cos x) +(1-cosx)/sin x$

$=(sinx*sinx+(1-cosx)(1-cosx))/(sinx(1-cos x))$ ->common denominator

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

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

$=(1+1-2cosx)/(sinx(1-cosx))$

$=(2-2cosx)/(sinx(1-cosx))$

$=(2(1-cosx))/(sinx(1-cosx))$

$=(2(cancel(1-cosx)))/(sinx cancel((1-cosx)))$

$=2/sinx$

$=2*1/sinx$

$=2 csc x$

$=RHS$

How do you verify sinx/(1-cosx) + (1-cosx)/sinx = 2cscxsinx/(1-cosx) + (1-cosx)/sinx = 2cscx?