Question

if sin alpha=1/2 and cos beta=√3/2, then find the value of sin(2 alpha+beta)

Answer 1

Answer:

$sin(2\alpha+\beta) = 1$

Step-by-step explanation:

It is given that: $sin\alpha=\frac{1}{2}$; therefore, $\alpha=30^o$.

It is also given that $cos\beta=\frac{\sqrt{3}}{2}$; therefore, $\beta=30^o$.

It is required to find: $sin(2\alpha+\beta)$.

$sin(2\alpha+\beta)\\ = sin(2(30^o)+30^o)\\=sin(90^o)\\=1$

Answer 2

Answer:

Given sinα= 1/2 and cosβ=√3/2

Step-by-step explanation:

For generalized case without any assumptions.

We need to find

Sin(2α+β)=?

[We use formula Sin(x+y)=Sinx.Cosy+Cosx.Siny]

We get,

Sin(2α+β)=Sin(2α).cos(β)+cos(2α).Sin(β)

Please check further solution in the pic attached.