Question

sin(alpha+2beta)= root3/2 ,cos(alpha+4 beta)=0. find alpha and beta

Answer 1

Answer:

give you an idea what the problem with you in advance of your assignment and it would take it off and it would make it

Answer 2

α = 30° and β = 15°

Step-by-step explanation:

We have,

$\sin(\alpha+2\beta)=\dfrac{\sqrt{3}}{2}$ and $\cos(\alpha+4 \beta)=0$

To find, the values of α and β = ?

∴  $\sin(\alpha+2\beta)=\dfrac{\sqrt{3}}{2}$

⇒ $\sin(\alpha+2\beta)=\sin 60$

⇒  α + 2β = 60°                     .........(1)

Also, $\cos(\alpha+4 \beta)=0$

⇒ $\cos(\alpha+4 \beta)=\cos 90$

⇒  α + 4β = 90°                     .........(2)

Subracting (1) from (2), we get

α + 4β - α - 2β = 90° - 60°

⇒ 2β = 30°

⇒  β = 15°

Put β = 15° in (1), we get

α + 2( 15°) = 60°

⇒ α = 60° - 30° = 30°

∴ α = 30° and β = 15°