Question

Sabendo que sen x= 3/5 determine tg 2x

Answer 1

sen²x + co²x = 1

(3/5)² + cos²x = 1

cos²x = 1 - 9/25

cos²x = (25 -9)/25

cos²x = 16/25

cosx = -4/5 ou cosx = 4/5

tgx =senx/cosx

tgx = 3/5/(-4/5) = 3/5.(-5/4) = -3/4
ou
tgx = 3/5/3/5 = 3/5.5/4 = 3/4

tg2x = 2tgx/(1-tg²x)

tg2x = 2.(-3/4) : (1 - 9/16)

tg2x = -3/2 : (7/16)

tg2x = -3/2.16/7

tg2x = -48/14

tg2x = -24/7

ou

tg2x = 2.3/4:(1 -9/16)

tg2x = 3/2 : 7/16

tg2x = 3/2.16/7

tg2x= 48/14

tg2x = 24/7