If tan θ + cot θ = 8, then what is the value of tan2 θ + cot2 θ ?

36 64 62 16

62

We are given that :- tan θ + cot θ = 8 On squaring both side, ( tan θ + cot θ )² = 8²  tan² θ + cot² θ + 2 tan θ . cot θ  = 64 tan² θ + cot² θ + 2  = 64  { tan θ = \(\frac{1}{cotθ}\) } tan² θ + cot² θ  = 62