Question

How do you verify `sin^2 ( x/2) = (cscx-cotx)/(2cscx)`?

Answer 1

RHS `=(cscx-cotx)/(2cscx)`
`=(sinx(cscx-cotx))/(2sinx*cscx)` Multiplying both numerator and denominator by sinx

`=(sinx*cscx-sinx*cotx)/2`
`=(1-cosx)/2=(2sin^2(x/2))/2`
`=sin^2(x/2)=LHS`

Proved