Question

how to prove trigonometric identity?

Answer 1

\[\sin 3 \alpha=\sin \left( 2 \alpha+\alpha \right)=?\]

Answer 2

4sin^3α

Answer 3

\[\sin \left( \alpha+\beta \right)=\sin \alpha \cos \beta+\cos \alpha \sin \beta\]

Answer 4

\[\sin \left( 2 \alpha+\alpha \right)=\sin 2 \alpha \cos \beta +\cos 2 \alpha \sin \beta \]
\[=2 \sin \alpha \cos \alpha \cos \alpha +\left( 1- 2\sin ^2 \alpha \right)\sin \alpha \]
\[=2 \sin \alpha \left( 1-\sin ^2 \alpha \right)+\sin \alpha - \sin ^3\alpha=?\]

Answer 5

correction
\[=2 \sin \alpha \left( 1-\sin ^2 \alpha \right)+\sin \alpha -2 \sin ^3 \alpha =?\]

Answer 6

4sin^3α ?