Question

Sabendo que sen x + cos x= 17/13, quanto vale sen 2x ?

Answer 1

Olá Leo
sen2x=2.senx.cosx
(senx+cosx)²=(17/13)²
sen²x+2.senx.cosx+cosx²=289/169
como 2.senx.cosx=sen2x
sen²x+sen2x+cos²x=289/169
sen²x+cos²x+sen2x=289/169
1+sen2x=289/169
sen2x=289/169-1
sen2x=289/169-169/169
sen2x=120/169
pronto

Answer 2

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$\sf sen(x)+cos(x)=\dfrac{17}{13}\\\sf [sen(x)+cos(x)]^2=\bigg[\dfrac{17}{13}\bigg]^2\\\sf sen^2(x)+2\cdot sen(x)\cdot cos(x)+cos^2(x)=\dfrac{289}{169}\\\sf sen^2(x)+cos^2(x)+sen(2x)=\dfrac{289}{169}\\\sf 1+sen(2x)=\dfrac{289}{169}\\\sf sen(2x)=\dfrac{289}{169}-1\\\sf sen(2x)=\dfrac{289-169}{169}\\\huge\boxed{\boxed{\boxed{\boxed{\sf sen(2x)=\dfrac{120}{169}}}}}\blue{\checkmark}$