Given:
The given expression is:
[tex]\dfrac{3\sin a-4\sin 4a}{\sin 5a}[/tex]
To find:
The value of the given expression at [tex]a=-45[/tex].
Solution:
We have,
[tex]\dfrac{3\sin a-4\sin 4a}{\sin 5a}[/tex]
Substituting [tex]a=-45[/tex], we get
[tex]\dfrac{3\sin (-45)-4\sin [4(-45)]}{\sin [5(-45)]}[/tex]
[tex]=\dfrac{-3\sin (45)+4\sin (180)}{-\sin (225)}[/tex]
[tex]=\dfrac{-3\sin (45)+4\sin (180)}{-\sin (180+45)}[/tex]
[tex]=\dfrac{-3\sin (45)+4\sin (180)}{\sin (45)}[/tex]
On substituting [tex]\sin (180)[/tex], we get,
[tex]=\dfrac{-3\sin (45)+4(0)}{\sin (45)}[/tex]
[tex]=\dfrac{-3\sin (45)+0}{\sin (45)}[/tex]
[tex]=\dfrac{-3\sin (45)}{\sin (45)}[/tex]
[tex]=-3[/tex]
Therefore, the value of the given expression at [tex]a=-45[/tex] is [tex]-3[/tex].
