lf \( tan \theta + cot \theta = 5 \), then \( tan^{2} \theta + cot^{2} \theta \) is:
Correct Answer: Description for Correct answer:
Given
\( tan \theta + cot \theta \) = 5
squaring on both sides, we have
\( \left(tan \theta +cot \theta \right)^{2}= \left(5\right)^{2} \)
\( tan^{2} \theta + cot^{2} \theta + 2 tan \theta .cot \theta = 25 \)
since, \( tan \theta = \frac{1}{cot \theta } \)
\( tan^{2} \theta +cot^{2} \theta = 25 - 2 = 23 \)
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