If `5 cos theta = 6 , sin theta `, evalutate :
`tan theta`

Answer

To solve the problem, we start with the given equation:

**Step 1: Write down the equation.**
We have:
\[ 5 \cos \theta = 6 \sin \theta \]

**Step 2: Rearrange the equation.**
We can rearrange this equation to express the ratio of sine and cosine:
\[ \frac{\sin \theta}{\cos \theta} = \frac{5}{6} \]

**Step 3: Recognize the definition of tangent.**
From trigonometry, we know that:
\[ \tan \theta = \frac{\sin \theta}{\cos \theta} \]

**Step 4: Substitute the ratio into the tangent definition.**
Now, substituting the ratio we found in Step 2 into the definition of tangent:
\[ \tan \theta = \frac{5}{6} \]

**Step 5: State the final answer.**
Thus, we have:
\[ \tan \theta = \frac{5}{6} \]

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