Please help to simplify as much as possible? #(1-cosx)/sinx +sinx/(1-cosx)#

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Answer 1 · 2018-02-27T00:48:10

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

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

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

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

#=2/sinx=2cscx#

Answer 2 · 2018-02-27T05:13:32

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

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

#=([1-2cosx+cos^2x] + sin^2x)/ (sinx(1-cosx))#

We know that, #sin^2x+cos^2x=1#

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

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

#=(2cancel((1-cosx)))/ (sinxcancel((1-cosx))#

#=2/sinx = 2cscx#