How do you prove $(1-cos(x)) / sin(x) = csc(x) - cot(x)$ ?

Question

10489 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-30T00:46:59

Recall the following identities:

$1. color(red)(cscx=1/sinx)$

$2. color(blue)(cotx=cosx/sinx)$

Given,

$(1-cosx)/sinx=cscx-cotx$

Simplify the right side.

$color(red)(cscx)-color(blue)(cotx)$

$=color(red)(1/sinx)-color(blue)(cosx/sinx)$

$=(1-cosx)/sinx$

$:.$ , LS $=$ RS.

How do you prove (1-cos(x)) / sin(x) = csc(x) - cot(x) (1-cos(x)) / sin(x) = csc(x) - cot(x) ?