Question #246a9

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Answer 1 · 2017-03-20T21:23:37

see below

Left Hand Side:

#color(red)(1 + tan^2theta/(sec theta+1)=color(blue)(1+(sin^2theta/cos^2theta)/(1/costheta+1)#

#color(blue)(=1+(sin^2theta/cos^2theta)/((1+costheta)/cos theta)#

#color(blue)(=1+sin^2theta/cos^2theta*(cos theta)/(1+costheta)#

#color(blue)(=1+sin^2theta/cos^cancel2theta*cancel(cos theta)/(1+costheta)#

#color(blue)(=1+sin^2theta/(costheta(1+costheta)#

#color(blue)(=(cos theta+cos^2 theta+sin^2theta)/(costheta(1+cos theta))#

#color(blue)(=(cos theta+1)/(cos theta(1+cos theta)#

#color(blue)(=(1+cos theta)/(cos theta(1+cos theta)#

#color(blue)(=cancel(1+cos theta)/(cos theta cancel((1+cos theta)#

#color(blue)(=1/cos theta#

#color(blue)( :. = sec theta#

Answer 2 · 2017-03-21T03:48:30

#LHS= 1 + tan^2theta/(sec theta+1)#

#= 1 + (sec^2theta-1)/(sec theta+1)#

#= 1 + ((cancel(sectheta+1))(sectheta-1))/(cancel(sec theta+1))#

#=1+sectheta-1=sectheta=RHS#