Discussion

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:

\(\tan^2 \theta + \cot^2 \theta + 2(1) = 4\)

\(\tan^2 \theta + \cot^2 \theta = 2\).

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