<p>In a triangle ABC, if \(\tan A = 2 \sin 2C\) and \(3 \cos A = 2 \sin B \sin C\) then possible values of C is/are:</p>
Step-by-Step Solution
Key Concept: Use the constraint equations along with A+B+C=π and trigonometric identities to solve for C
<p>From the first equation: \(\tan A = 4\sin C \cos C\)</p><p>Using \(A + B + C = \pi\), we have \(B = \pi - A - C\)</p><p>Substitute into the second equation and simplify using trigonometric identities.</p><p>After algebraic manipulation, this yields \(C = \frac{\pi}{4}\) as a valid solution.</p><p>Checking: when \(C = \frac{\pi}{4}\), the conditions are satisfied.</p>
Correct Answer: C