Question

expresar en términos de una sola función
1 + tg^2
sen^2x + cos^2x + tg^2x
csc^2x - cot^2 x + tg^2x
tgx cotx - cot^2 + tg^2x
sen^2 (csc^2x - cot^2x)/ cosx*secx

Answer 1

DESARROLLO:

Antes de comenzar debemos saber que :

${tan}^{2} (x) + 1 = {sec}^{2} (x)$

${cot}^{2} (x) + 1 = {cosc}^{2} (x)$

${sen}^{2} (x) + {cos}^{2} (x) = 1$

Entonces:

Primero:

${tan}^{2} (x) + 1$

${sec}^{2} (x)$

Segundo:

${sen}^{2} (x) + {cos}^{2} (x) + {tan}^{2} (x)$

$1 + {tan}^{2} (x)$

${sec}^{2} (x)$

Tercero:

${cosc}^{2} (x) - {cot}^{2} (x) + {tan}^{2} (x)$

$1 + {tan}^{2} (x)$

${sec}^{2} (x)$

Cuarto:

$\frac{ {sen}^{2}(x)( {cosc}^{2}(x) - {cot}^{2} (x)) }{cos(x) \times sec(x)}$

$\frac{1 - {cos}^{2}(x) }{1}$

${sen}^{2} (x)$

Un gusto espero que te sirva.