3 years ago

Someone solve this please.

Mathematics

1 answer:

laila [671]3 years ago

7 0

The answer is one hundred

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Ierofanga [76]

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,

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

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

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

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

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