How do you prove 2tanxcsc2x-(tan^2)x=1?

Unsure of which identities to use and how.

1 Answer
Aug 5, 2017

See below

Explanation:

We shall use the following identities:

#tanA-=sinA/cosA#

#cscA-=1/sinA#

#secA-=1/cosA#

#sin2A-=2sinAcosA#

#sec^2A-tan^2A-=1#

Proof

#2tanxcsc2x-tan^2x#

#=(2sinx)/(cosxsin2x)-tan^2x#

#=(2sinx)/(2cos^2xsinx)-tan^2x#

#=sec^2x-tan^2x#

#=1#

#therefore LHS=RHS# #QED#