Question

Question #887ef

Answer 1

`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

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