Question

If tan A + cot A = 2, then the value of tan⁴ A + cot⁴ A =

• A. 2
• B. 1
• C. 4
• D. 5

Answer 1

The Correct Option is A

Given tan A + cot A = 2. Since \(\cot A = \frac{1}{\tan A}\), we can rewrite the given equation as: \(\tan A + \frac{1}{\tan A} = 2\)

Let \(x = \tan A\). 

Then \(x + \frac{1}{x} = 2\). 

Multiplying by \(x\) gives \(x^2 + 1 = 2x\), or \(x^2 - 2x + 1 = 0\). 

This factors as \((x-1)^2 = 0\), so \(x=1\). Thus, \(\tan A = 1\), which implies \(\cot A = \frac{1}{\tan A} = 1\).

Now, tan⁴ A + cot⁴ A = 1⁴ + 1⁴ = 1 + 1 = 2.

Answer: (A) 2