Question

sabendo que cosx=1/5 e x E 1º Q, determine: sen 2x; cos 2x; tg 2x

Answer 1

* sen2x = 2senxcosx

* sen²x + cos²x = 1
sen²x = 1 - cos²x
senx = √(1 - cos²x)

Portanto, sen2x = 2.√(1 - cos²x) . cosx
sen2x = 2√(1 - (1/5)²) .1/5
sen 2x = 2/5 √(1 - 1/25)
sen2x = 2/5√(24/25)
sen2x = (2/5) .(2/5)√6
sen2x = (4√6)/25

cos2x = cos²x - sen²x
cos2x = 1/25 - 96/25
cos2x = - 95/25
cos2x = 19/5

(tgx = senx/cosx e senx = 2√6/5)

tg2x = (2tgx)/ (1 -tg²x)
tg2x =( 2senx/cosx)(1 - sen²x/cos²x)

substituindo os valores:

tg2x = (-4√6)/23