If \(\sin \theta = \cos \theta\), then the value of \(2\tan \theta + \cos^2 \theta\) is:
Answer: D
If \(\sin \theta = \cos \theta\), dividing both sides by \(\cos \theta\) gives \(\tan \theta = 1\). This means \(\theta = 45°\).
Now we evaluate the expression: \(2\tan 45° + \cos^2 45°\).
= \(2(1) + (\frac{1}{\sqrt{2}})^2\)
= \(2 + \frac{1}{2} = \frac{5}{2}\).