How do you prove #1-cosx^2/(1+sinx)= sinx#?

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Answer 1 · 2015-04-15T14:40:11

Solution

#1-(cos^2x)/(1+sinx)=sinx....(i)#

As

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

So,

L.H.S of equation no. #(i)#

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

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

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

#=1-(1-sinx)#

#=1-1+sinx#

#=cancel1-cancel1+sinx#

#=sinx#

#=R.H.S#