Question

If tanθ + cotθ = 2 and θ is acute, then the value of tan100θ + cot100θ is equal to:

Answer 1

Correct Answer - Option 3 : 2

Given:

tanθ + cotθ = 2

Calculation:

Put the value of θ = 45^o, tan45^o = 1, and cot45^o = 1

Then, tanθ + cotθ = 2

⇒ tan45^o + cot45^o = 2

⇒ 1 + 1 = 2

putting the value θ = 45 in tan100θ + cot100θ

⇒ tan¹⁰⁰45 + cot¹⁰⁰45 

⇒ 1¹⁰⁰ + 1¹⁰⁰

⇒ 2

∴ The value of tan100θ + cot100θ is 2.