If \(\sin\theta + \cos\theta = \sqrt{2}\cos\theta\), where \(0 < \theta < 90°\), then the value of \(\tan\theta\) is:
\(\sqrt{2} - 1\)
Starting with \(\sin\theta + \cos\theta = \sqrt{2}\cos\theta\), rearrange to get \(\sin\theta = \sqrt{2}\cos\theta - \cos\theta = (\sqrt{2} - 1)\cos\theta\).
Dividing both sides by \(\cos\theta\): \(\tan\theta = \sqrt{2} - 1\).
Hence, the value of \(\tan\theta\) is \(\sqrt{2} - 1\).
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