if cot thetha= 4/3 then the value of cos thetha - sin thetha ÷ cos thetha+ sin thetha
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if cot thetha= 4/3 then the value of cos thetha - sin thetha ÷ cos thetha+ sin thetha
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To find the value of \(\frac{{\cos(\theta) - \sin(\theta)}}{{\cos(\theta) + \sin(\theta)}}\) when \(\cot(\theta) = \frac{4}{3}\), you can use trigonometric identities.
First, you can use the definition of \(\cot(\theta)\) to find \(\cos(\theta)\) and \(\sin(\theta)\). \(\cot(\theta) = \frac{4}{3}\) implies that \(\frac{\cos(\theta)}{\sin(\theta)} = \frac{4}{3}\), so \(\cos(\theta) = 4k\) and \(\sin(\theta) = 3k\), where \(k\) is a constant.
Now, substitute these values into the expression:
\[
\frac{\cos(\theta) - \sin(\theta)}{\cos(\theta) + \sin(\theta)} = \frac{4k - 3k}{4k + 3k} = \frac{k}{7k} = \frac{1}{7}
\]
So, when \(\cot(\theta) = \frac{4}{3}\), the value of \(\frac{\cos(\theta) - \sin(\theta)}{\cos(\theta) + \sin(\theta)}\) is \(\frac{1}{7}\).