Tan θ + Cot θ = 2, then Tan^2 θ + Cot^2 θ = A) 4 B) 2 C) 6 D) 1
Tan θ + Cot θ = 2, then Tan2 θ + Cot2 θ =
A) 4
B) 2
C) 6
D) 1
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Correct option is: B) 2
We have Tan \(\theta\) + Cot \(\theta\) = 2
= \((tan \, \theta + cot \, \theta)^2 = 2^2 = 4 \)
= \(tan^2\theta + cot^2\theta + 2 \,tan \, \theta \, cot \, \theta = 4 \) (\(\because\) \((a+b)^2 = a^2+b^2 + 2ab\))
= \(tan^2\theta + cot^2\theta + 2 = 4\) (\(\because\) cot \(\theta\) \(\frac 1{tan \, \theta} =\) tan \(\theta\) cot \(\theta\) =1)
= \(tan^2\theta + cot^2\theta = 4-2 =2\)
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