Resolver 2tan2(1+operatorname{ctan}2)^2

$$2 \tan 2 ( 1 + \operatorname { ctan } 2 ) ^ { 2 }$$

Ebaluatu

$$\frac{2\tan(2)\left(\sin(2)c+\cos(2)\right)^{2}}{\left(\cos(2)\right)^{2}}$$

Ebazpidea

\left(1+c\tan(2)\right)^{2} zabaltzeko, erabili Newton-en binomioa \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

$$2\tan(2)\left(1+2c\tan(2)+c^{2}\left(\tan(2)\right)^{2}\right)$$

Erabili banaketa-propietatea 2\tan(2) eta 1+2c\tan(2)+c^{2}\left(\tan(2)\right)^{2} biderkatzeko.

$$2\tan(2)+4\left(\tan(2)\right)^{2}c+2c^{2}\left(\tan(2)\right)^{3}$$

Diferentziatu c balioarekiko

$$\frac{4\left(\tan(2)\right)^{2}\left(\sin(2)c+\cos(2)\right)}{\cos(2)}$$