How do you verify $cscx-1=cot^2x/(cscx+1)$ ?

Question

6936 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-12T14:47:43

$1/sinx - 1 = (cos^2x/sin^2x)/(1/sinx+ 1)$

$1/sinx- sinx/sinx= (cos^2x/sin^2x)/((1 + sinx)/sinx)$

$(1 - sinx)/sinx= cos^2x/sin^2x xx sinx/(1 + sinx)$

$(1 - sinx)/sinx= (1 - sin^2x)/sinx xx 1/(1 + sinx)$

$(1 - sinx)/sinx = ((1 + sinx)(1 - sinx))/sinx xx 1/(1 + sinx)$

$(1- sinx)/sinx = (1 - sinx)/sinx$

$LHS = RHS$

Identity Proved!

Hopefully this helps!

How do you verify cscx-1=cot^2x/(cscx+1)cscx-1=cot^2x/(cscx+1)?