Question

Chứng minh:

Nếu sin(2a + b) = 3sinb; cos(a + b) khác 0 thì tan(a + b) = 2tana.

Answer 1

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

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

\(\Leftrightarrow sina.cos\left(a+b\right)+cosa.sin\left(a+b\right)=3sin\left(a+b\right)cosa-3cos\left(a+b\right)sina\)

\(\Leftrightarrow4cos\left(a+b\right).sina=2sin\left(a+b\right)cosa\)

\(\Leftrightarrow\dfrac{2sina}{cosa}=\dfrac{sin\left(a+b\right)}{cos\left(a+b\right)}\)

\(\Leftrightarrow2tana=tan\left(a+b\right)\)