If \(\tan \theta + \cot \theta = 2\), what is the value of \(\tan^2 \theta + \cot^2 \theta\)?
Answer: B
We are given \(\tan \theta + \cot \theta = 2\). Squaring both sides:
\((\tan \theta + \cot \theta)^2 = 2^2\)
\(\tan^2 \theta + \cot^2 \theta + 2 \tan \theta \cot \theta = 4\)
Since \(\tan \theta \cot \theta = 1\), the equation becomes:
\(\tan^2 \theta + \cot^2 \theta + 2(1) = 4\)
\(\tan^2 \theta + \cot^2 \theta = 2\).