(1-cosx)/sinx + sinx/(1-cosx) = 2/sinx1−cosxsinx+sinx1−cosx=2sinx
Left Side :=(1-cosx)/sinx + sinx/(1-cosx) =1−cosxsinx+sinx1−cosx
=((1-cosx)(1-cos x) + sinx*sinx)/(sinx(1-cosx))=(1−cosx)(1−cosx)+sinx⋅sinxsinx(1−cosx)
=(1-2cosx+cos^2x+sin^2x)/(sinx(1-cosx))=1−2cosx+cos2x+sin2xsinx(1−cosx)
=(1-2cosx+1)/(sinx(1-cosx))=1−2cosx+1sinx(1−cosx)
=(2-2cosx)/(sinx(1-cosx))=2−2cosxsinx(1−cosx)
=(2(1-cosx))/(sinx(1-cosx))=2(1−cosx)sinx(1−cosx)
=(2cancel((1-cosx)))/(sinxcancel((1-cosx)))
=2/sinx
:.= Right Side