How do I prove that #2/(cotxtan2x) -= 1 - tan^2x#?

Question

1446 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-20T14:09:05

As proved below.

#cot x = 1/ tan x#

# tan 2x = (2 tan x) / (1 - tan^2 x)# - Identity.

To prove #2 / (cot x * tan 2x) = 1 - tan^2 x#

#2 / (cot x * tan 2x)#

=> (2 tan x) / tan 2x#

#=> (2 tan x) / ((2tan x) / (1 - tan^2 x))#

#=> (1 - tan^2 x) = R H S#