Question

Find acute angles A and B, if $\sin \left(A+2B\right)=\frac{\sqrt{3}}{2}\mathrm{and}\cos \left(A+4B\right)=0,A>B$.

Answer 1

Given:

…… (1)

…… (2)

We know that,

…… (3)

…… (4)

Now by comparing equation (1) and (3)

We get,

…… (5)

Now by comparing equation (2) and (4)

We get,

…… (6)

Now to get the values of A and B, let us solve equation (5) and (6) simultaneously

Therefore by subtracting equation (5) from (6)

We get,

Therefore,

Hence

Now by multiplying equation (5) by 2

We get,

…… (7)

Now by subtracting equation (6) from (7)

We get,

Therefore,

Hence

Therefore the values of A and B are as follows and