Hello,
We have the equation:
( Cosx + Cosx.tg^2x).Secx
We know too:
Tgx = Senx/Cosx
Then,
Cosx.Tg^2x = Cosx . Sen^2x / cos^2x
= Sen^2x/cosx
Then, we stay with:
(Cosx + Sen^2x/Cosx) . Secx
There is a trigonometric property that says:
Sec x = 1 / Cosx
Then, this mean:
Secx = 1 / cos x
Then,
( Cosx + Sen^2/Cosx). 1/Cosx
Applying the distributive:
Cosx . 1/Cosx + Sen^2x / Cos^2x
Simplifying Cos x/ cosx
1 + Sen^2x / Cos^2x
Rewrinting Sen^2x/Cos^2x = Tg^2x
Then us stay:
= 1 + Tg^2x = Sec^2x <=> I hope this has helped
