Question

Mostre que 1 + 1/tg²x = 1/sen²x

Answer 1

$1/senx^{2} = 1 + \frac{1}{tg^{2}x }\\\\1 + \frac{1}{tg^{2}x } = \frac{tg^{2}x + 1}{tg^{2}x } = \frac{\frac{sen^{2} + cos^{2}x}{cos^{2}x} }{tg^{2}x } = \frac{\frac{1}{cos^{2}x} }{tg^{2}x } = \frac{\frac{1}{cos^{2}x} }{\frac{sen^{2} x}{cos^{2}x} } = \frac{1}{sen^{2}x}$

Answer 2

Resposta:

Explicação passo-a-passo:

sen²x + cos²x = 1, divide tudo por sen²x.

sen²x/sen²x + cos²x/sen²x = 1/sen²x

1 + cotg²x = cossec²x

1 + 1/tg²x = 1/sen²x