Question
If tan θ + cot θ = 16, then find the value of
tan2θ + cot2θ.Solution
We know that, (a + b) 2 = a2 + b2 + 2ab
So, (tan θ + cot θ) 2 = tan2 θ + cot2 θ + 2 x tan θ x cot θ
So, 162 = tan2 θ + cot2 θ + (2 x 1)
So, tan2 θ + cot2 θ = 256 - 2 = 254
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