Question

AYUDA CON ESTE EJERCICIO DE TRIGO ​

Answer 1

Respuesta:

5/13

Explicación paso a paso:

*se sabe:

cos²60=1/4

sen²60=3/4

sec²60=4

sec²45=2

csc⁴45=4

*resolviendo:

$\frac{tg\beta-cos^{2}60}{sen^{2}60+tg\beta}=\frac{sec^{2}45-tg\beta(sec^{2}60)}{sec^{2}60-tg\beta(csc^{4}45)}$

$\frac{tg\beta-(1/4)}{(3/4)+tg\beta}=\frac{2-4tg\beta}{4-4tg\beta}$

$\frac{4tg\beta-1}{3+4tg\beta}=\frac{1-2tg\beta}{2-2tg\beta}$

$2(1-tg\beta)(4tg\beta-1)=(3+4tg\beta)(1-2tg\beta)$

$2(4tg\beta-1-4tg^{2}\beta+tg\beta)=3-6tg\beta+4tg\beta-8tg^{2}\beta$

$2(5tg\beta-1-4tg^{2}\beta)=3-2tg\beta-8tg^{2}\beta$

$10tg\beta-2-8tg^{2}\beta=3-2tg\beta-8tg^{2}\beta$

$10tg\beta-2=3-2tg\beta$

$12tg\beta=5$

$tg\beta=5/12$  

∴ senβ=5/13