Question

If $ \tan \theta + \cot \theta = 4 $, then find the value of $ \tan^3 \theta + \cot^3 \theta $.

• A. 52
• B. 44
• C. 46
• D. 54

Hint:

To evaluate \( \tan^3 \theta + \cot^3 \theta \), use the identity: \[ a^3 + b^3 = (a + b)^3 - 3ab(a + b) \] Also, convert to a single variable using substitution like \( \tan \theta = x \Rightarrow \cot \theta = \frac{1}{x} \).