Question

Verifique a identidade trigonométrica : (1+cotg²x).(1-cos²x)= 1

Answer 1

$(1 + cotg^2x)\cdot(1-cos^2x) = 1$

Substituindo:

cos²x + sen²x = 1 → sen²x = 1 - cos²x
cotg²x = cos²x/sen²x


$(1 + \frac{cos^2x}{sen^2x} )\cdot(sen^2x) = 1 \\ \\ ( \frac{sen^2x}{sen^2x} + \frac{cos^2x}{sen^2x} ) \cdot sen^2x = 1 \\ \\ ( \frac{sen^2x + cos^2x}{sen^2x} ) \cdot sen^2x = 1 \\ \\ \boxed{\boxed{sen^2x + cos^2x = 1}}$