Question

If tan α + cot α = 2, then tan²⁰α + cot²⁰α = ______.

Options

• 0

• 2

• 20

• 2²⁰

Answer 1

If tan α + cot α = 2, then tan²⁰α + cot²⁰α = 2.

Explanation:

Given: tan α + cot α = 2

To find: tan²⁰ α + cot²⁰ α

Step 1: Use the identity

Let: x = tan α,then cot α = `1/x`

So, the equation becomes: `x + 1/x = 2`

Multiply both sides by x: 

x² + 1 = 2x ⇒ x² − 2x + 1 = 0 ⇒ (x − 1)² = 0 ⇒ x = 1

So: tan α = 1 ⇒ cot α = 1

Step 2: Substitute into the target expression

tan²⁰ α + cot²⁰ α = 1²⁰ + 1²⁰ = 1 + 1 = 2