Prove the identity (1-tan^2x)/(1+tan^2x) is same as 1-2sin^2x?

1 Answer
Somebody N.
Nov 14, 2017

See below.

Explanation:

Using Identities:

#color(red)(tan^2x=sin^2x/cos^2x)#

#color(red)(sin^2x+cos^2x=1)#
..................................................................................................................................

#LHS#

#(1-(sin^2x)/cos^2x)/(1+sin^2x/cos^2x)#

Multiply by #cos^2x#:

#(cos^2x-sin^2x)/(cos^2x+sin^2x)#

#color(red)(sin^2x+cos^2x=1)#

#cos^2x-sin^2xcolor(white)(88)# ( #cos^2x= 1-sin^2x# )

#1-sin^2x-sin^2x#

#1-2sin^2x#

#LHS -=RHS#

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