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Answer 1 · 2018-02-14T22:34:12

See below.

RHS:

#(1-tan^2y)/(1+tan^2y)#

Identity:

#color(red)(bbtanx=sinx/cosx)#

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

Add fractions:

#((cos^2y-sin^2y)/cos^y)/((cos^2y+sin^2y)/(cos^2y))=(cos^2y-sin^2y)/(cos^2y+sin^2y)#

Identity:

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

&# color(white)(88)color(red)(bb(sin^2x=1-cos^2x)#

#(cos^2y-(1-cos^2y))/1#

#cos^2y-1+cos^2y#

#2cos^2y-1#

Identity:

#color(red)bb(cos2x=2cos^2x-1)#

Hence:

#cos2y#

#RHS-=LHS#