Prove? #sinx/(1-cosx)-(1+cosx)/sinx=0#

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Answer 1 · 2017-08-14T03:41:53

I'll try to answer this, assuming that the question is:

#sinx/(1-cosx)-(1+cosx)/sinx=0#

We need a common denominator, so I'll work with the left hand fraction first:

#sinx/(1-cosx)(1)-(1+cosx)/sinx=0#

#sinx/(1-cosx)((1+cosx)/(1+cosx))-(1+cosx)/sinx=0#

#(sinx(1+cosx))/(1-cos^2x)-(1+cosx)/sinx=0#

Remember that #sin^2x+cos^2x=1 => sin^2x=1-cos^2x#

#(sinx(1+cosx))/sin^2x-(1+cosx)/sinx=0#

#(1+cosx)/sinx-(1+cosx)/sinx=0#

#0=0 color(white)(000)color(green)root#