Question

se a tgx= -3 determine o cosx sendo x arco do 2° quadrante.​

Answer 1

tgx = -3

tg²x = 9

(1) +tg²x = (1)+ 9

sec²x = 10

secx = -√10

1/secx = -1/√10

cosx = -√10/ 10 <=======©

Answer 2

${ \sec}^{2}x = 1 + { \tan }^{2}x \\ { \sec }^{2}x = 1 + {( - 3)}^{2} \\ { \sec }^{2}x = 1 + 9 \\ { \sec }^{2}x = 10$

$\sec(x) = - \sqrt{10}$

$\cos(x) = \frac{1}{ \sec(x) } \\ \cos(x) = - \frac{1}{ \sqrt{10} } = - \frac{ \sqrt{10} }{10}$