Question #887ef

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Answer 1 · 2017-05-15T05:23:10

#LHS=(sin^2x +4sinx +3)/cos^2x#

#=(sin^2x +3sinx+sinx +3)/(1-sin^2x)#

#=(sinx(sinx+3)+1xx(sinx+3))/((1-sinx)(1+sinx))#

#=((sinx+3)(sinx+1))/((1-sinx)(1+sinx))#

#= (3+sinx)/(1-sinx)=RHS#

Proved

Answer 2 · 2017-05-15T05:25:27

see below

We use RHS to prove LHS

multiply with #(1 + sin x)#

#(3 + sin x)/(1 - sinx) * (1 + sin x)/(1 + sin x)#

#= (3 + 3 sin x + sin x + sin^2 x)/(1 - sin^2x)#

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

#= (3 + 4 sin x + sin^2 x)/ cos^2 x#--->proved