Correct Answer - Option 4 : 34
Given:
tan θ + cot θ = 6
Formula Used:
(a + b)2 = a2 + b2 + 2ab
tanθ × cotθ = 1
Calculations:
tan θ + cot θ = 6
Squaring both sides, we get
(tan θ + cot θ)2 = (6)2
⇒ tan2 θ + cot2 θ + 2 × tanθ × cotθ = 36
⇒ tan2 θ + cot2 θ + 2 × 1 = 36
⇒ tan2 θ + cot2 θ = 36 – 2
⇒ tan2 θ + cot2 θ = 34
∴ The value of tan2 θ + cot2 θ is 34.