Question

The value of \(\tan \left(\frac{\pi}{4} + \theta \right) \cdot \tan \left(\frac{3\pi}{4} + \theta \right)\) is

• A. 1
• B. 2
• C. -1
• D. 0

Hint:

Use the trigonometric identities to simplify the expression.

Answer 1

The Correct Option is C

We can use the identity for tangent addition: \[ \tan(A + B) \cdot \tan(A - B) = 1 \] In this case, we have: \[ \tan \left(\frac{\pi}{4} + \theta \right) \cdot \tan \left(\frac{3\pi}{4} + \theta \right) = -1 \] Thus, the correct answer is -1.