The value of $\tan(\pi/4 + \theta) \tan(3\pi/4 + \theta)$ is
- A. -2
- B. 2
- C. 1
- D. -1
✅ Correct Answer: -1
Explanation
$\tan(\pi/4 + \theta) = (1 + \tan\theta)/(1 - \tan\theta)$ $\tan(3\pi/4 + \theta) = (-1 + \tan\theta)/(1 + \tan\theta)$ Multiplying $= (1 + \tan\theta)/(1 - \tan\theta) \times (-1 + \tan\theta)/(1 + \tan\theta)$ $= -1$
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