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Given that 5 sin x + 4 cos x = 0, find the value of tan x

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We can start by rearranging the equation 5 sin x + 4 cos x = 0 by dividing both sides by cos(x):

5

sin

cos

+

4

=

0

5

cosx

sinx

+4=0

Recall that $\frac{\sin x}{\cos x} = \tan x$. So we can substitute this in:

5

tan

+

4

=

0

5tanx+4=0

Now we can solve for $\tan x$:

\begin{align*}

5 \tan x + 4 &= 0 \

5 \tan x &= -4 \

\tan x &= \frac{-4}{5}

\end{align*}

Therefore, the value of $\tan x$ is $\boxed{\frac{-4}{5}}$.

Given that 5 sin x + 4 cos x = 0, find the value of tan x-example-1
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