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

Question

4911 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-25T07:22:49

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

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