#(2tan theta)/(1+tan^2 theta)#?

1 Answer
maganbhai P.
Mar 12, 2018

#2sinthetacostheta=sin2theta#

Explanation:

#(2tantheta)/(1+tan^2theta)=(2color(blue)((sintheta/costheta)))/(1+(color(blue)(sin^2theta/cos^2theta)))#.....where, #color(blue)(tantheta=(sintheta/costheta))#
#=((2sintheta)/costheta)/(color(red)((cos^2theta+sin^2theta))/cos^2theta)#...#where,##color(red)(sin^2theta+cos^2theta=1)#
#=((2sintheta)/costheta)/((color(red)( 1 ))/cos^2theta)#
#=2*sintheta/cancel(costheta)*cos^cancel(2)theta#
#=2sinthetacostheta#
#=sin2theta#

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