Question

2.- Demostrar que: (1- Cos² A) Ctg²A = Cos² A​

Answer 1

Respuesta:

(1- Cos² A) Ctg²A = Cos² A​

1- cos²A + 1- ctg²A   (cos²A+ ctg²A= 1 Por lo tanto: cos²A = 1- ctg²A)

Cos² A  

Answer 2

Respuesta:

Explicación paso a paso:

$(1-\cos^{2}(A))\cot^{2}(A)=\cos^{2}(A)\\\\\boxed{\cot^{2}(A)=\frac{\cos^{2}(A)}{\sin^{2}(A)}\, (*) }\\\boxed{\sin^{2}(A)=1-\cos^{2}(A)\,(**)}\\\texttt{Usando (*) y (**); y simplificando nos queda:}\\\\(1-\cos^{2}(A))\cot^{2}(A)=(1-\cos^{2}(A))\frac{\cos^{2}(A)}{\sin^{2}(A)}=\\\\=(1-\cos^{2}(A))\frac{\cos^{2}(A)}{1-\cos^{2}(A)}=\cos^{2}(A)$