Question #897a1

1 Answer
Nov 17, 2016

see below

Explanation:

(1-cosx)/sinx + sinx/(1-cosx) = 2/sinx1cosxsinx+sinx1cosx=2sinx

Left Side :=(1-cosx)/sinx + sinx/(1-cosx) =1cosxsinx+sinx1cosx

=((1-cosx)(1-cos x) + sinx*sinx)/(sinx(1-cosx))=(1cosx)(1cosx)+sinxsinxsinx(1cosx)

=(1-2cosx+cos^2x+sin^2x)/(sinx(1-cosx))=12cosx+cos2x+sin2xsinx(1cosx)

=(1-2cosx+1)/(sinx(1-cosx))=12cosx+1sinx(1cosx)

=(2-2cosx)/(sinx(1-cosx))=22cosxsinx(1cosx)

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

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

=2/sinx

:.= Right Side