Question

Reduce:

A = (1 - sen^2x)(1+ tan^2x)(1 - cos^2x)(1 + cot^2x)

Help me

Answer 1

Respuesta:

Explicación paso a paso:

Saludos

Recuerda:

$Sen^{2} \beta+Cos^{2} \beta =1\left \{ {{Sen^{2} \beta =1-Cos^{2}\beta } \atop {Cos^{2} \beta =1-Sen^{2} \beta }} \right.$

$Sec^{2} \beta-Tan^{2} \beta =1\left \{ {{Sec^{2} \beta =1+Tan^{2}\beta } \atop {Tan^{2} \beta= Sec^{2} \beta -1} \right.$

$Csc^{2} \beta-Cot^{2} \beta =1\left \{ {{Csc^{2} \beta =1+Cot^{2}\beta } \atop {Cot^{2} \beta =Csc^{2} \beta -1} \right.$

En el problema: Calcular:

$A=(1-Sen^{2} x)(1+Tan^{2} x)(1-Cos^{2} x)(1+Cot^{2} x)$

$A=(Cos^{2} x)(Sec^{2} x)(Sen^{2} x)(Csc^{2} x)$

$A=(\frac{1}{Sec^{2} x} )(Sec^{2} x)(\frac{1}{Csc^{2} x} )(Csc^{2} x)$

Simplificamos:

$A=(1)(1)(1)(1)$

$A=1$