Question #16fc9

2 Answers
Aug 23, 2017

See Below

Explanation:

LHS:
#=(1+sin x)/cos x * ( 1-sin x)/(1-sin x)#

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

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

#=cos^cancel (2) x /(cancel(cos x)(1-sin x))#

#=cos x/ (1-sin x)#

#:.=#RHS

Aug 23, 2017

See the proof below

Explanation:

We need

#cos^2x+sin^2x=1#

Therefore,

#LHS=(1+sinx)/cosx#

#=((1+sinx)(1-sinx))/(cosx(1-sinx))#

#=((1-sin^2x))/(cosx(1-sinx))#

#=((cos^2x))/(cosx(1-sinx))#

#=cosx/(1-sinx)#

#=RHS#

#QED#