Goniometria

Uno alla volta vedi regolamento! Comunque li svolgo.

204)

ricorda che sen^2(α) + cos^2(α) = 1;

tan(α) = sen(α) / cos(α).

sen^2(α) - 1 - 4 [tan^2(α) +1] * sen^2(α)=

= 1 - cos^2(α) - 1 - 4 [(sen^2(α) / cos^2(α)  + 1] * sen^2(α)=

= - cos^2(α) - 4 * [(sen^2(α) + cos^2(α) )/ cos^2(α)] * sen^2(α) =

= - cos^2(α) - 4 * [1 * sen^2(α)/ cos^2(α)] =

= - cos^2(α) -   4 sen^2(α)/[cos^2 (α)] =

= {- [cos^2(α)]^2 - 4 sen^2(α)} / [cos^2(α)] =

= {- [cos^2(α)]^2 - 4 * [1 - cos^2(α)]} / [cos^2 (α)] =

= {- [cos^2 (α)]^2 - 4 + 4 cos^2 (α)} / [cos^2 (α)] =

= - {[cos^2 (α)]^2 + 4 - 4 cos^2(α)} / cos^2(α) =

= - [cos^2 (α) - 2]^2 / cos^2(α).

Ciao @daniele01953

211

sen(α) / [cos(α)sen(α) cos^2(α)]  + sen(α) cos(α) / cos(α) - {[sen^2(α)/cos^2(α)] + 1} / cos(α) =

= 1/[cos^3(α)] + sen(α) - [sen^2(α) + cos^2(α)] / [ cos^3(α)] =

= 1/[cos^3(α)] + sen(α) - 1/[cos^3(α)] =

= sen(α).

@daniele01953 ciao 

Uno alla volta vedi regolamento!

204)

ricorda che sen^2(α) + cos^2(α) = 1;

tan(α) = sen(α) / cos(α).

sen^2(α) - 1 - 4 [tan^2(α) +1] * sen^2(α)=

= 1 - cos^2(α) - 1 - 4 [(sen^2(α) / cos^2(α)  + 1] * sen^2(α)=

= - cos^2(α) - 4 * [(sen^2(α) + cos^2(α) )/ cos^2(α)] * sen^2(α) =

= - cos^2(α) - 4 * [1 * sen^2(α)/ cos^2(α)] =

= - cos^2(α) -   4 sen^2(α)/[cos^2 (α)] =

= {- [cos^2(α)]^2 - 4 sen^2(α)} / [cos^2(α)] =

= {- [cos^2(α)]^2 - 4 * [1 - cos^2(α)]} / [cos^2 (α)] =

= {- [cos^2 (α)]^2 - 4 + 4 cos^2 (α)} / [cos^2 (α)] =

= - {[cos^2 (α)]^2 + 4 - 4 cos^2(α)} / cos^2(α) =

= - [cos^2 (α) - 2]^2 / cos^2(α).

Ciao @daniele01953