If \(\alpha+\beta=\displaystyle\frac{\pi}{2}\) and \(\alpha:\beta=2:1\), then what is the ratio of \(\tan\alpha\) to \(\tan\beta\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(3:1\)
\(\frac{\pi}{2}\) is \(90^\circ\). Dividing \(90^\circ\) in the ratio \(2:1\) gives the two angles, and both have standard tangent values.
\(\alpha=\displaystyle\frac{2}{3}\times 90^\circ=60^\circ\) and \(\beta=\displaystyle\frac{1}{3}\times 90^\circ=30^\circ\)
\(\tan 60^\circ=\sqrt{3}\) and \(\tan 30^\circ=\displaystyle\frac{1}{\sqrt{3}}\)
\(\tan\alpha:\tan\beta=\sqrt{3}:\displaystyle\frac{1}{\sqrt{3}}=3:1\)