Question

Tg² A = (1 + Tg² A) (1 - Cos² A)​

Answer 1

Respuesta:

$T=\frac{1-\cos ^2\left(A\right)}{g^2A\cos ^2\left(A\right)};\quad \:g\ne \:0$

Explicación paso a paso:

$Tg^2A=1-\cos ^2\left(A\right)+g^2AT-g^2AT\cos ^2\left(A\right)$

$Tg^2A-\left(g^2AT-g^2AT\cos ^2\left(A\right)\right)=1-\cos ^2\left(A\right)+g^2AT-g^2AT\cos ^2\left(A\right)-\left(g^2AT-g^2AT\cos ^2\left(A\right)\right)$

$g^2AT\cos ^2\left(A\right)=1-\cos ^2\left(A\right)$

$T=\frac{1-\cos ^2\left(A\right)}{g^2A\cos ^2\left(A\right)};\quad \:g\ne \:0$

Answer 2

Respuesta:

$Tg^2 A\\\\\frac{sen^2A}{cos^2A} \\\\(\frac{1}{cos^2A}) \times (sen^2A )\\\\(\frac{sen^2A+cos^2A}{cos^2A} )\times (1-cos^2A)\\\\(\frac{sen^2A}{cos^2A} +\frac{cos^2A}{cos^2A} )\times (1-cos^2A)\\\\(Tg^2A+1)\times (1-cos^2A)\\\\\boxed {(1+Tg^2A)(1-cos^2A)}$