Answer:
Step-by-step explanation:
Sin t . Sin 3t . Sin 5t = 1/4 [ - Sin t + Sin 3t + Sin 7t - Sin 9t ]
Take Right hand side and use the following formula
[tex]sin C - sin D = 2 Cos\left ( \frac{C+D}{2} \right )Sin\left ( \frac{C-D}{2} \right )[/tex]
[tex]Cos C - Cos D = 2 Sin\left ( \frac{C+D}{2} \right )Sin\left ( \frac{D-C}{2} \right )[/tex]
Take right hand side
[tex]\frac{1}{4}\left (Sin 3t - Sin t + Sin 7t - Sin 9t \right )[/tex]
[tex]\frac{1}{4}\left (2 Cos 2t Sin t +2 Sin (-t)Cos 8t \right )[/tex]
[tex]\frac{1}{4}\times 2 Sin t\left (Cos 2t-Cos8t \right )[/tex]
[tex]\frac{1}{4}\times 2 Sin t\ \times 2 \times Sin 5t\times 3t[/tex]
Sin t . Sin 3t . Sin 5t
So, LHS = RHS
