Question #887ef

2 Answers
May 15, 2017

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

May 15, 2017

see below

Explanation:

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