Question

If tanθ + cotθ = 5, then the value of tan2 θ+ cot2 θ is

Answer 1

${( \tan \theta + \cot\theta) }^{2} = {5}^{2} \\ { \tan}^{2} \theta + 2 \tan\theta \cot\theta + { \cot }^{2} \theta = 25 \\ { \tan}^{2} \theta + { \cot }^{2} \theta = 25 - 2 = 23$