If \(1 + sin^2 \ \theta = 3 sin \ \theta \ cos \ \theta\), then prove that \(tan \ \theta = 1\) or \(\frac{1}{2}\).
Proof:
Given that \(1 + sin^2 \ \theta = 3 sin \ \theta \ cos \ \theta\).
Dividing both sides by \(sin^2 \ \theta\) then we get,
\(1 + cot^2 \ \theta + 1\) =
By simplyfing this then we get,
\(cot \ \theta=\) (or) \(cot \ \theta=\)
[Note: Enter the answer in ascending order]
Therefore the value of \(tan \ \theta=1\) (or) \(tan \ \theta=\frac{1}{2}\)
Hence proved.
Answer variants:
\(2\)
\(\frac{3}{4}\)
\(1\)
\(cosec^2 \ \theta + 1 = \frac{3 cos \ \theta}{sin \ \theta}\)
\(3 cot \ \theta\)