Question

Sin t sin 3t sin 5t = 1/4(-sin t + sin 3t +sin 7t - sin 9t).

Answer 1

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

`sin C - sin D = 2 Cos\left ( (C+D)/(2) \right )Sin\left ( (C-D)/(2) \right )`

`Cos C - Cos D = 2 Sin\left ( (C+D)/(2) \right )Sin\left ( (D-C)/(2) \right )`

Take right hand side

`(1)/(4)\left (Sin 3t - Sin t + Sin 7t - Sin 9t  \right )`

`(1)/(4)\left (2 Cos 2t Sin t +2 Sin (-t)Cos 8t \right )`

`(1)/(4)* 2 Sin t\left (Cos 2t-Cos8t \right )`

`(1)/(4)* 2 Sin t\ * 2 * Sin 5t* 3t`

Sin t . Sin 3t . Sin 5t

So, LHS = RHS