Question

If tan θ + cot θ = 2 and 0° < θ < 90° then tan¹⁰ θ + cot¹⁰ θ is equal to ______.

Answer 1

If tan θ + cot θ = 2 and 0° < θ < 90° then tan¹⁰ θ + cot¹⁰ θ is equal to 2.

Explanation:

 Let t = tan θ.

Then `t + 1/t = 2`

⇒ t² + 1 = 2t 

⇒ (t – 1)² = 0 

So t = 1 and θ = 45° since 0° < θ < 90°. 

Therefore tan¹⁰ θ + cot¹⁰ θ

= 1¹⁰ + 1¹⁰

= 1 + 1

= 2