Question

(EEAR) A expressão 1+cotg²x/1+tg²x é identica ao: A) tg²x B) sen²x C) cotg²x D) cos²x

Answer 1

$\frac{1+cotg^2(x)}{1+tg^2x}=\\ \\ \frac{1+\frac{cos^2x}{sen^2x}}{1+\frac{sen^2(x)}{cos^2(x)}}=\\ \\ \frac{\frac{sen^2x+cos^2x}{sen^2x}}{\frac{cos^2(x)+sen^2x}{cos^2(x)}}=\\ \\ \frac{\frac{1}{sen^2(x)}}{\frac{1}{cos^2(x)}}=\frac{1}{sen^2(x)}*\frac{cos^2(x)}{1}=\frac{cos^2(x)}{sen^2(x)}=cotg^2(x)$