How do you verify? 1-cos(x)/sin(x)+sin(x)/1+cos(x)=2cscx

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Answer 1 · 2018-02-28T04:48:41

#(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#

Hence Proved.