Question

If (tan θ + cot θ) = 5 then the value of (tan²θ + cot²θ) is ______.

Options

• 23

• 24

• 25

• 27

Answer 1

If (tan θ + cot θ) = 5 then the value of (tan²θ + cot²θ) is 23.

Explanation:

(tan θ + cot θ)² = 5² = 25

⇒ tan²θ + cot²θ + 2 = 25

∴ (tan²θ + cot²θ) = (25 – 2) = 23.