Question

Nếu \(5\sin\alpha=3\sin\left(\alpha+2\beta\right)\)thì \(\tan\left(\alpha+\beta\right)\)=???

Answer 1

\(5sina=3sin\left(a+2b\right)\)

\(\Leftrightarrow5sin\left(a+b-b\right)=3sin\left(a+b+b\right)\)

\(\Leftrightarrow5sin\left(a+b\right)cosb-5cos\left(a+b\right)sinb=3sin\left(a+b\right)cosb+3cos\left(a+b\right)sinb\)

\(\Leftrightarrow2sin\left(a+b\right).cosb=8cos\left(a+b\right)sinb\)

\(\Leftrightarrow\frac{sin\left(a+b\right)}{cos\left(a+b\right)}=\frac{4sinb}{cosb}\)

\(\Leftrightarrow tan\left(a+b\right)=4tanb\)