If Tan θ + Cot θ = 5, then the value of Tan^2 θ + Cot^2 θ = A) 25 B) 23 C) 27 D) 15
If Tan θ + Cot θ = 5, then the value of Tan2 θ + Cot2 θ =
A) 25
B) 23
C) 27
D) 15
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Correct option is: B) 23
Given that tan \(\theta\) + Cot \(\theta\) = 5
= \((tan \, \theta + cot \, \theta)^2 = 5^2 = 25\)
= \(tan^2\theta + cot^2\theta + 2\, tan \, \theta. cot\, \theta =25 \) (\(\because\) \((a+b)^2 = a^2 + b^2 + 2ab\))
= \(tan^2\theta + cot^2\theta + 2 =25 \)( \(\because\) cot \(\theta\) = \(\frac 1{tan\, \theta}\) = tan \(\theta\) - cot \(\theta\) = 1)
= \(tan^2\theta + cot^2\theta =25 -2 = 23\)
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