Question

Fie x un nr real care verifica egalitatea tg x+ctg x=4. Calculati sin 2x. Multumesc!

Answer 1

tg x+ctg x=4 ⇔ sinx/cosx + cosx/sinx = 4⇔ (sin²x + cos²x)/(sinxcosx) =4 ⇔

⇔ 1/(sinxcosx) =4 ⇔ sinxcosx = 1/4 |·2 ⇔ 2sinxcosx = 1/2 ⇔ sin2x = 1/2