Discussion

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 = \(3 \times (\frac{5}{3})^2 = 3 \times \frac{25}{9} = \frac{25}{3}\).

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