Question

Please help

prove the identity
sin(x)/1-cos(x)+sin(x)/1+cos(x)=2csc(x)

Answer 1

sin(x)/1 - cos(x) + sin(x) /1 + cos(x) Lets take LCM of Denominators

sinx ( 1 + cosx) + sinx(1-cosx)/(1 - cos^2x)
sinx + sinxcosx + sinx - sinxcosx/sin^2x (Since sin^2x = 1- cos^2x)
2sinx/sin^2x = 2/sinx = 2cosec(x) (Since 1/sinx = cosecx)