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pochemuha
2 years ago
8

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

Mathematics
1 answer:
Ierofanga [76]2 years ago
8 0

Given:

The given expression is:

\dfrac{3\sin a-4\sin 4a}{\sin 5a}

To find:

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

Solution:

We have,

\dfrac{3\sin a-4\sin 4a}{\sin 5a}

Substituting a=-45, we get

\dfrac{3\sin (-45)-4\sin [4(-45)]}{\sin [5(-45)]}

=\dfrac{-3\sin (45)+4\sin (180)}{-\sin (225)}

=\dfrac{-3\sin (45)+4\sin (180)}{-\sin (180+45)}

=\dfrac{-3\sin (45)+4\sin (180)}{\sin (45)}

On substituting \sin (180), we get,

=\dfrac{-3\sin (45)+4(0)}{\sin (45)}

=\dfrac{-3\sin (45)+0}{\sin (45)}

=\dfrac{-3\sin (45)}{\sin (45)}

=-3

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

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