If \(\cos X = 3/5\), then the value of \(3 + 3\tan^2 X\) is:
Answer: C
First, we can factor out the 3 from the expression: \(3(1 + \tan^2 X)\).
Using the Pythagorean identity \(1 + \tan^2 X = \sec^2 X\), the expression simplifies to \(3 \sec^2 X\).
We are given \(\cos X = 3/5\). Since \(\sec X = 1/\cos X\), we have \(\sec X = 5/3\).
Now substitute this value into the expression:
Value = \(3 \times (\frac{5}{3})^2 = 3 \times \frac{25}{9} = \frac{25}{3}\).