If \(\sin\theta + \cos\theta = \sqrt{2}\), then find the value of \(\tan\theta + \cot\theta\).
2
Squaring: \(1 + 2\sin\theta\cos\theta = 2 \Rightarrow \sin\theta\cos\theta = \frac{1}{2}\)
\(\tan\theta + \cot\theta = \frac{\sin^2\theta + \cos^2\theta}{\sin\theta\cos\theta} = \frac{1}{\sin\theta\cos\theta} = \frac{1}{1/2} = 2\)
Hence, the answer is 2.
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