If \(\sin\theta + \cos\theta = \frac{7}{17}\), then find the positive value of \(\sin\theta - \cos\theta\).
Squaring: \((\sin\theta + \cos\theta)^2 = \frac{49}{289} \Rightarrow 1 + 2\sin\theta\cos\theta = \frac{49}{289}\)
\(2\sin\theta\cos\theta = \frac{49}{289} - 1 = -\frac{240}{289}\)
\((\sin\theta - \cos\theta)^2 = 1 - 2\sin\theta\cos\theta = 1 + \frac{240}{289} = \frac{529}{289}\)
Positive value: \(\sin\theta - \cos\theta = \frac{23}{17}\)
Hence, the answer is \(\frac{23}{17}\).
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