Question

3sina-4sin4a/sin5a
if a=-45 degree

Answer 1

Given:

The given expression is:

`(3\sin a-4\sin 4a)/(\sin 5a)`

To find:

The value of the given expression at
`a=-45`.

Solution:

We have,

`(3\sin a-4\sin 4a)/(\sin 5a)`

Substituting
`a=-45`, we get

`(3\sin (-45)-4\sin [4(-45)])/(\sin [5(-45)])`

`=(-3\sin (45)+4\sin (180))/(-\sin (225))`

`=(-3\sin (45)+4\sin (180))/(-\sin (180+45))`

`=(-3\sin (45)+4\sin (180))/(\sin (45))`

On substituting
`\sin (180)`, we get,

`=(-3\sin (45)+4(0))/(\sin (45))`

`=(-3\sin (45)+0)/(\sin (45))`

`=(-3\sin (45))/(\sin (45))`

`=-3`

Therefore, the value of the given expression at
`a=-45` is
`-3`.